In this paper, we consider a global regulation problem of a class of nonlinear systems that have uncertain high-order nonlinear terms. In particular, we introduce new high-order lower triangular and non-triangular conditions and propose a controller with dynamic gains to regulate the system with uncertain high-order nonlinearities. In designing our controller, the information of the growth rate is not required, and the forms of the high-order nonlinearities are more relaxed. We verify that the proposed method is applicable to the system which cannot be regulated by the existing methods. Examples and simulation results are given for clear illustration. Copyright © 2016 John Wiley & Sons, Ltd.

This paper investigates the problem of adaptive event-triggering scheme for networked interconnected systems to relieve the burden of the network bandwidth. The data releasing is triggered by an adaptive event-triggering device. The triggering condition depends on the state information at both the latest releasing instant and the current sampling instant. The threshold of the triggering parameter is achieved online rather than a predetermined constant. Taking the network-induced delays and the coupling delays of the subsystems into account, together with the hybrid adaptive event-triggering scheme and the stochastic uncertainty, we propose an unified model of the networked interconnected system. Sufficient conditions for the mean square stability and stabilization of the interconnected systems are developed by using Lyapunov–Krasovskii functional approach. A co-designed method is put forward to obtain the controller gains and the weight of the triggering condition simultaneously. Finally, an example is provided to demonstrate the design method. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, adaptive output feedback control for a class of nonlinear systems with quantized input is investigated. The nonlinearities of the nonlinear systems under consideration are assumed to satisfy linear growth condition on the unmeasured states multiplied by unknown growth rate and output polynomial function. By developing a dynamic high-gain observer, a linear-like output feedback controller is constructed, with which it is proved that the output of the quantized control system can be steered to within an arbitrarily small residual set while keeping all the other closed loop states bounded. In particular, if the growth rate is known, it is proved that all the states of the system can be steered to within an arbitrarily small neighborhood of the origin. Copyright © 2016 John Wiley & Sons, Ltd.

This paper addresses the problem of output feedback sampled-data stabilization for upper-triangular nonlinear systems with improved maximum allowable transmission delay. A class of hybrid systems are firstly introduced. The transmission delay may be larger than the sampling period. Then, sufficient conditions are proposed to guarantee global exponential stability of the hybrid systems. Based on these sufficient conditions and a linear continuous-discrete observer, an output feedback control law is presented to globally exponentially stabilize the feedforward nonlinear system. The improved maximum allowable transmission delay is also given. The results are also extended to output feedback sampled-data stabilization for lower-triangular nonlinear systems. Finally, illustrative examples are used to verify the effectiveness of the proposed design methods. Copyright © 2016 John Wiley & Sons, Ltd.

We consider an automatic control system with relay nonlinearity and sinusoidal external influence. Sufficient conditions for the existence of periodic solutions in the case when the characteristic equation of the system has complex roots are obtained. We use an approach that permits to investigate the system analytically and prove the existence of at least one periodic solution (including asymptotically stable solution) with the period multiple to the period of external influence and two switching points on the phase plane. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we aim at addressing the problem of global output feedback stabilization for a class of uncertain nonlinear systems with quantized input and output. The nonlinear functions of the system are assumed to satisfy high-order growth condition on the unmeasurable states. Based on the homogeneous domination approach and sector bound approach, a homogeneous quantized controller computed from quantized output is constructed, and a guideline is derived to select the parameters of the quantizers. Further, it is proved that, with the proposed scheme, the closed-loop system is globally asymptotically stable. Copyright © 2016 John Wiley & Sons, Ltd.

This paper studies the robustness of model-based event-triggered control systems with respect to the differences between the plant and model matrices. Two types of event conditions, which involve an additional threshold variable and the norm of model states, are investigated, respectively. The tunable parameters in both the event conditions are designed according to the differences between the plant and model matrices. Also, the uncertainties in the plant matrices are considered, and the asymptotic stability can be guaranteed robustly. Moreover, the relationship between the tunable parameters and the model matrices is revealed. Namely, on the one hand, there exists a range of the tunable parameters such that the closed-loop system is asymptotically stable with model matrices in any compact set. On the other hand, if the differences between the plant and model matrices are small enough, the tunable parameters can be set arbitrarily large. Finally, a numerical example is provided to illustrate the efficiency and feasibility of the obtained results. Copyright © 2016 John Wiley & Sons, Ltd.

In this work, the controllability of single-leader multi-agent systems with chain structures is studied. It is shown that the necessary and sufficient condition for the multi-chain system to be controllable is that there exist no two chain lengths in the form *ℓ*_{1}=*i* + *k*_{1}(2*i* + 1) and *ℓ*_{2}=*i* + *k*_{2}(2*i* + 1), where *i* is some natural number and *k*_{1} and *k*_{2} some nonnegative integers. Using this condition, the author derives an upper bound based on the length of the longest chain and proves that if the number of chains exceeds this bound, the multi-chain system must be uncontrollable. In addition, the author investigates an augmented system constructed by connecting some follower nodes of the multi-chain system and obtains a sufficient condition for the augmented system to be uncontrollable. Finally, the author shows how to select a minimum number of additional leaders to make an uncontrollable multi-chain system controllable. Numerical examples are provided to illustrate the results. Copyright © 2016 John Wiley & Sons, Ltd.

This article extends two recent contributions in the field of quantitative feedback theory to the multivariable case. They concern the model matching and the measured disturbance rejection problems. The model matching problem is a tracking control problem with specifications given as acceptable deviations from an ideal response. The measured disturbance rejection problem balances feedback and feedforward actions to reject disturbances. Both perspectives present advantages over classical quantitative feedback theory techniques in certain situations. This paper develops the necessary tools to solve both control problems in the case of multi-input multi-output plants. In particular, it shows how to derive nonconservative controller bounds for each of the single-input single-output control problems in which the overall multivariable problem is divided. The result is a systematic controller design methodology for multi-input multi-output plants with structured uncertainty. The application of the technique to the well-known quadruple-tank process illustrates the benefits of the method. Copyright © 2016 John Wiley & Sons, Ltd.

The possibility of mismatch between prior uncertainty modeling assumptions and reality is a problem both for robust control and for model-based adaptive control algorithms that aim to use real-time data to adaptively identify and correct such problems. Mismatches between prior model assumptions may fool adaptive algorithms intended to improve robustness into persistently preferring destabilizing controllers over stabilizing ones even when the instability is patently obvious to the eyes of the most casual observer. To eliminate all possibility of being thusly fooled, the assumption-free unfalsified control concept was introduced in the early 1990s and has since been developed to the point where it now provides a unifying overarching theoretical framework for understanding the relationships, benefits, and weakness of various adaptive control methods. We review how the theory allows one to parsimoniously sift the individual elements of accumulating evidence and experimental data to determine precisely which of the elements falsify a given performance level and very briefly discuss recent research on cost-detectable fading-memory cost functions for time-varying plants. Copyright © 2016 John Wiley & Sons, Ltd.

This paper investigates the problem of stabilizing a time-varying nonlinear sampled-data system based on its approximate models. Given a time-varying nonlinear sampled-data system, we make use of the approximate models of the system at each sampling instant to build a time-varying approximate model with which an appropriate controller is designed. This paper provides some sufficient conditions under which a controller stabilizing the approximate models can also stabilize the exact sampled-data system under any sufficiently small sampling period. With this method, we do not need to compute the complicated exact discrete-time model of the concerned system and significantly simplify the controller design. The major contribution of this method lies in extending the available results regarding the time-invariant sampled-data systems to the time-varying case. Moreover, this method enables us to analyze the influence of the precision of approximate models on the system performance. Copyright © 2016 John Wiley & Sons, Ltd.

This paper is concerned with the *H*_{∞} performance analysis for networked control systems with transmission delays and successive packet dropouts under stochastic sampling. The parameter uncertainties are time-varying norm-bounded and appear in both the state and input matrices. If packet loss is considered the same as time delay, when models the networked control systems with successive packet dropouts and delays as ordinary linear system with input-delay approach, due to sampling period is stochastic, then the delay caused by packet losses is a stochastic variable, which leads to difficulties in the stability analysis of the considered system. However, if we can transform the system with stochastic delay into a continuous system with stochastic parameter, we can solve the problem. In this paper, by assuming that the network packet loss rate and employing the information of probabilistic distribution of the time delays, the stochastic sampling system is transformed into a continuous-time model with stochastic variable, which satisfies a Bernoulli distribution. By linear matrix inequality approach, sufficient conditions are obtained, which guarantee the robust mean-square exponential stability of the system with an *H*_{∞} performance. What's more, an *H*_{∞} controller design procedure is then proposed, and a less conservative result is obtained by taking the probability into consideration. Finally, a numerical simulation example is employed to show the effectiveness of the obtained results. Copyright © 2016 John Wiley & Sons, Ltd.

This paper formulates and addresses the problem of equivalence in terms of multistability properties between nonlinear models of gene regulatory systems of different dimensionality. Given a nonlinear dynamical model of a gene regulatory network and the structure of another higher-dimensional gene regulatory network, the aim is to find a dynamical model for the latter that has the same equilibria and stability properties as the former. We propose construction rules for the dynamics of a high-dimensional system, given the low-dimensional system and the high-dimensional network structure. These construction rules yield a multistability-equivalent system, as we prove in this work. We demonstrate the value of our method by applying it to an example of a multistable gene regulatory network involved in mesenchymal stem cell differentiation. Here, differentiation is described by a core motif of three genetic regulators, but the detailed network contains at least nine genes. The proposed construction method allows to transfer the multistability based differentation mechanism of the core motif to the more detailed gene regulatory network. Copyright © 2016 John Wiley & Sons, Ltd.

The by-now standard formulation of interconnection and damping assignment passivity-based control (for input-affine systems) proposes the solution of a partial differential equation (PDE) that defines the assignable energy functions and computes the control using the input matrix pseudo-inverse. However, in its original formulation—a *more general* design procedure was proposed, which was essentially abandoned because of the difficulties in solving the PDE. In this note, a new family of interconnection and damping assignment passivity-based controls is proposed by extending this method in the following directions: (i) It allows the desired interconnection and damping matrices to depend on the control signal, giving the possibility to *shape the PDE* to ensure its solvability; (ii) the PDE directly generates the control signal that have, in general, simpler expressions; and (iii) it is applicable for general nonlinear systems possibly not affine in the control. The technique is illustrated with three examples, including the well-known boost power converter for which it yields a simple, high-performance controller. Copyright © 2016 John Wiley & Sons, Ltd.

This paper is concerned with the finite-time guaranteed cost control problem for stochastic Markovian jump systems with incomplete transition rates. By a mode-dependent approach (MDA), several new sufficient conditions for the existence of state and output feedback finite-time guaranteed cost controllers are provided, and the upper bound of cost function is more accurately expressed. Moreover, these results' superiorities are analyzed and shown. A new N-mode optimization algorithm is given to minimize the upper bound of cost function. Finally, a detailed example is utilized to demonstrate the merit of the proposed results. Copyright © 2016 John Wiley & Sons, Ltd.

This paper considers the receding horizon tracking control of the unicycle-type robot subject to coupled input constraint based on virtual structure. The tracking position of the follower is considered to be a virtual structure point with respect to a Frenet–Serret frame fixed on the leader, and the desired control input of the follower not only depend on the input of the leader but also the separation vector. Firstly, a sufficient input condition for the leader robot is given to enable the follower to track its desired position while satisfying its inputs constraint. Secondly, receding horizon control scheme is designed for the follower robot, in which the recursive feasibility is guaranteed by developing a diamond-shaped positively invariant terminal-state region and its corresponding controller. Finally, simulation results are provided to verify the effectiveness of the scheme proposed. Copyright © 2016 John Wiley & Sons, Ltd.

The attitude tracking of a rigid body without angular velocity measurements is addressed. A continuous angular velocity observer with fractional power functions is proposed to estimate the angular velocity via quaternion attitude information. The fractional power gains can be properly tuned according to a homogeneous method such that the estimation error system is uniformly *almost* globally finite-time stable, irrespective of control inputs. To achieve output feedback attitude tracking control, a quaternion-based nonlinear proportional-derivative controller using full-state feedback is designed first, yielding uniformly *almost* globally finite-time stable of the attitude tracking system as well as bounded control torques *a priori*. It is then shown that the certainty equivalent combination of the observer and nonlinear proportional-derivative controller ensures finite-time convergence of the attitude tracking error for *almost* all initial conditions. The proposed methods not only avoid high-gain injection, as opposed to the semi-global results, but also overcome the unwinding problem associated with some quaternion-based observers and/or controllers. Numerical simulations are presented to verify the effectiveness of the proposed methods.

This paper addresses the asymptotic stability and *L*_{∞}-gain analysis problem for a class of nonlinear positive systems with both unbounded discrete delays and distributed delays. With the assumption that the nonlinear function is strictly increasing, we first give a characterization on the positivity of the nonlinear system. Then, with some mild assumptions on the delays, a necessary and sufficient condition to ensure the asymptotic stability is presented. Moreover, an explicit expression of the *L*_{∞}-gain of such nonlinear positive systems is given in terms of the system matrices. Finally, a numerical example is given to illustrate the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we consider the stability issue of economic model predictive control (EMPC) for constrained nonlinear systems and propose a new contractive constraint formulation of nonlinear EMPC schemes. This formulation is one of Lyapunov-based approaches in which the contractive function chosen a priori can be used as a Lyapunov function. Some conditions are given to guarantee recursive feasibility and asymptotic stability of the EMPC. Moreover, we analyze the transient economic performance of the EMPC closed-loop system in some finite-time intervals. The proposed EMPC scheme is applied to a chemical reactor model to illustrate its utility and benefits.

In this paper, we claim the availability of deterministic noises for stabilization of the origins of dynamical systems, provided that the noises have unbounded variations. To achieve the result, we first consider the system representations of rough systems based on rough path analysis; then, we provide the notion of asymptotic stability for rough systems to analyze the stability for the systems. In the procedure, we also confirm that the system representations include stochastic differential equations; we also found that asymptotic stability for rough systems is the same property as uniform almost sure asymptotic stability provided by Bardi and Cesaroni. After the discussion, we confirm that there is a case that deterministic noises are capable of making the origin become asymptotically stable for rough systems while stochastic noises do not achieve the same stabilization results. Copyright © 2016 John Wiley & Sons, Ltd.

This paper studies bipartite consensus problems for continuous-time multi-agent system over signed directed graphs. We consider general linear agents and design both state feedback and dynamic output feedback control laws for the agents to achieve bipartite consensus. Via establishing an equivalence between bipartite consensus problems and the conventional consensus problems under both state feedback and output feedback control approaches, we make direct application of existing state feedback and output feedback consensus algorithms to solve bipartite consensus problems. Moreover, we propose a systematical approach to design bipartite consensus control laws. Copyright © 2016 John Wiley & Sons, Ltd.

This paper focuses on the analysis and the design of event-triggering scheme for discrete-time systems. Both static event-triggering scheme (SETS) and adaptive event-triggering scheme (AETS) are presented for discrete-time nonlinear and linear systems. What makes AETS different from SETS is that an auxiliary dynamic variable satisfying a certain difference equation is incorporated into the event-triggering condition. The sufficient conditions of asymptotic stability of the closed-loop event-triggered control systems under both two triggering schemes are given. Especially, for the linear systems case, the minimum time between two consecutive control updates is discussed. Also, the quantitative relation among the system parameters, the preselected triggering parameters in AETS, and a quadratic performance index are established. Finally, the effectiveness and respective advantage of the proposed event-triggering schemes are illustrated on a practical example. Copyright © 2016 John Wiley & Sons, Ltd.

Integral inequalities have been widely used in stability analysis for systems with time-varying delay because they directly produce bounds for integral terms with respect to quadratic functions. This paper presents two general integral inequalities from which almost all of the existing integral inequalities can be obtained, such as Jensen inequality, the Wirtinger-based inequality, the Bessel–Legendre inequality, the Wirtinger-based double integral inequality, and the auxiliary function-based integral inequalities. Based on orthogonal polynomials defined in different inner spaces, various concrete single/multiple integral inequalities are obtained. They can produce more accurate bounds with more orthogonal polynomials considered. To show the effectiveness of the new inequalities, their applications to stability analysis for systems with time-varying delay are demonstrated with two numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.

The robustness properties of a first-order sliding-mode controller are combined with those of an added linear term in order to obtain a closed loop that shows input-to-state stability with respect to matched and unmatched disturbances, of which an upper bound might not be known, using only output information. The output under consideration can have any relative degree. Also, a transformation of the state into a novel output normal form is presented. The zero dynamics are considered unstable and perturbed, so a methodology for defining an observer and a virtual control for it is presented. Copyright © 2016 John Wiley & Sons, Ltd.

We study in this paper the problem of iterative feedback gains auto-tuning for a class of nonlinear systems. For the class of input–output linearizable nonlinear systems with bounded additive uncertainties, we first design a nominal input–output linearization-based robust controller that ensures global uniform boundedness of the output tracking error dynamics. Then, we complement the robust controller with a model-free *multi-parametric extremum seeking* control to iteratively auto-tune the feedback gains. We analyze the stability of the whole controller, that is, the robust nonlinear controller combined with the multi-parametric extremum seeking model-free learning algorithm. We use numerical tests to demonstrate the performance of this method on a mechatronics example. Copyright © 2016 John Wiley & Sons, Ltd.

Exponential stability necessary conditions for linear periodic time-delay systems are presented. They are obtained with the help of new properties of the Lyapunov matrix in the framework of Lyapunov–Krasvoskii functionals of complete type. An academic example illustrates our results. Copyright © 2016 John Wiley & Sons, Ltd.

Reset control techniques have been proposed to overcome fundamental limitations of linear controllers by means of their transformation into hybrid models that combine continuous flow and discrete jump dynamics. The hybrid nature in the control loop involves some difficulties when analyzing the performance of the controller and some drawbacks on the controller design related to the stability conditions. The technique that we propose is based on sector confined target dynamics of the continuous flow mode by means of the application of the discrete reset jumps. This behavior, in the error plane , is correlated with certain preferred sectors that lead to fast and over-damped responses. The paper studies how to design a hybrid resetting version of a linear controller that achieves the required fast and over-damped responses to arbitrary references. Copyright © 2016 John Wiley & Sons, Ltd.

Intensive research in the field of mathematical modeling of pneumatic servo drives has shown that their mathematical models are nonlinear in which many important details cannot be included in the model. Owing the influence of the combination of heat coefficient, unknown discharge coefficient, and change of temperature, it was supposed that parameters of the pneumatic cylinder are random (stochastic parameters). On the other side, it has been well known that the nonlinear model can be approximated by a linear model with time-varying parameters. Due to the aforementioned reasons, it can be assumed that the pneumatic cylinder model is a linear stochastic model with variable parameters. In practical conditions, in measurements, there are rare, inconsistent observations with the largest part of population of observations (outliers). Therefore, synthesis of robust algorithms is of primary interest. In this paper, the robust recursive algorithm for output error models with time-varying parameters is proposed. The convergence property of the proposed robust algorithm is analyzed using the methodology of an associated ordinary differential equation system. Because *ad hoc* selection of model orders leads to overparameterization or parsimony problem, the robust Akaike's criterion is proposed to overcome these problems. By determining the least favorable probability density for a given class of probability distribution represents a base for design of the robust version of Akaike's criterion. The behavior of the proposed robust identification algorithm is considered through intensive simulations that demonstrate the superiority of the robust algorithm in relation to the linear algorithms (derived under an assumption that the stochastic disturbance has a Gaussian distribution). The good practical values of the proposed robust algorithm to identification of the pneumatic cylinder are illustrated by experimental results. Copyright © 2016 John Wiley & Sons, Ltd.

In networked systems, intermittent failures in data transmission are usually inevitable due to the limited bandwidth of the communication channel, and an effective countermeasure is to add redundance so as to improve the reliability of the communication service. This paper is concerned with the model predictive control (MPC) problem by using static output feedback for a class of polytopic uncertain systems with redundant channels under both input and output constraints. By utilizing the min–max control approach combined with stochastic analysis, sufficient conditions are established to guarantee the feasibility of the designed MPC scheme that ensures the robust stability of the closed-loop system. In terms of the solution to an auxiliary optimization problem, an easy-to-implement MPC algorithm is proposed to obtain the desired sub-optimal control sequence as well as the upper bound of the quadratic cost function. Finally, to illustrate its effectiveness, the proposed design method is applied to control a networked direct current motor system. Copyright © 2016 John Wiley & Sons, Ltd.

This paper presents an online recorded data-based design of composite adaptive dynamic surface control for a class of uncertain parameter strict-feedback nonlinear systems, where both tracking errors and prediction errors are applied to update parametric estimates. Differing from the traditional composite adaptation that utilizes identification models and linear filters to generate filtered modeling errors as prediction errors, the proposed composite adaptation integrates closed-loop tracking error equations in a moving time window to generate modified modeling errors as prediction errors. The time-interval integral operation takes full advantage of online recorded data to improve parameter convergence such that the application of both identification models and linear filters is not necessary. Semiglobal practical asymptotic stability of the closed-loop system is rigorously established by the time-scales separation and Lyapunov synthesis. The major contribution of this study is that composite adaptation based on online recorded data is achieved at the presence of mismatched uncertainties. Simulation results have been provided to verify the effectiveness and superiority of this approach. Copyright © 2016 John Wiley & Sons, Ltd.

A modification of the particle filter algorithm that allows using it also in cases with incorrect measurements has been presented in the paper. The use of anti-zero bias does not require a large computational effort (a single additional operation for each measurement value), and simultaneously does not deteriorate results for the case of good measurements (if the bias value is not too large). It has been shown that the bias which provides the best estimation quality depends on the particles number. The obtained results have been compared with unscented Kalman filter method with bad measurement data identification. As an object, power system has been used, with main task set as estimation of the state of this system. Copyright © 2016 John Wiley & Sons, Ltd.

This paper investigates the exponential observer design problem for one-sided Lipschitz nonlinear systems. A unified framework for designing both full-order and reduced-order exponential state observers is proposed. The developed design approach requires neither scaling of the one-sided Lipschitz constant nor the additional quadratically inner-bounded condition. It is shown that the synthesis conditions established include some known existing results as special cases and can reduce the intrinsic conservatism. For design purposes, we also formulate the observer synthesis conditions in a tractable LMI form or a Riccati-type inequality with equality constraints. Simulation results on a numerical example are given to illustrate the advantages and effectiveness of the proposed design scheme. Copyright © 2016 John Wiley & Sons, Ltd.

This paper is concerned with the problem of finite-time asynchronous filtering for a class of discrete-time Markov jump systems. The communication links between the system and filter are assumed to be unreliable, which lead to the simultaneous occurrences of packet dropouts, time delays, sensor nonlinearity and nonsynchronous modes. The objective is to design a filter that ensures not only the mean-square stochastic finite-time bounded but also a prescribed level of performance for the underlying error system over a lossy network. With the help of the Lyapunov–Krasovskii approach and stochastic analysis theory, sufficient conditions are established for the existence of an admissible filter. By using a novel simple matrix decoupling approach, a desired asynchronous filter can be constructed. Finally, a numerical example is presented and a pulse-width-modulation-driven boost converter model is employed to demonstrate the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.

We consider almost output synchronization for directed heterogeneous time-varying networks where agents are non-introspective (i.e., agents have no access to their own states or outputs) in the presence of external disturbances. The nonlinear agents have a triangular structure and are globally Lipschitz continuous. The network can be time-varying with network switches occurring at arbitrary moments. A purely decentralized time-invariant protocol based on a low-gain and high-gain method is designed for each agent to achieve almost output synchronization while reducing the impact of disturbances on the output synchronization error. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, a boundary controller with disturbance observer is proposed for the vibration suppression of an axially moving belt system. The model of the belt system is described by a nonhomogeneous partial differential equation and a set of ordinary differential equations with consideration of the high-acceleration/deceleration and unknown spatiotemporally varying distributed disturbance. Applying the finite-dimensional backstepping control and Lyapunov's direct method, a boundary controller is developed to stabilize the belt system at the small neighborhood of its equilibrium position and a disturbance observer is introduced to attenuate the effect of unknown external disturbance. The S-curve acceleration/deceleration method is adopted to plan the speed of the belt. With the proposed control scheme, the spillover instability problems are avoided, the uniform boundedness and the stability of the closed-loop belt system can be achieved. Simulations are provided to illustrate the effectiveness of the proposed control scheme. Copyright © 2016 John Wiley & Sons, Ltd.

The technique of linear matrix inequalities is a powerful method for solving optimization problems. In this paper, a sliding function vector was calculated using linear matrix inequalities approach. This technique provided optimal values of the coefficients of the sliding function vector, which led to the reduction of the reachability phase. Then, a discrete second-order sliding mode control for multivariable systems was developed using this optimal sliding function vector. Two examples were used in order to illustrate the effectiveness of the proposed strategy. Simulation results prove good performances in terms of reduction of the reachability phase. Copyright © 2016 John Wiley & Sons, Ltd.

A distributed controller is developed that yields cooperative containment control of a network of autonomous dynamical systems. The networked agents are modeled with uncertain nonlinear Euler–Lagrange dynamics affected by an unknown time-varying exogenous disturbance. The developed continuous controller is robust to input disturbances and uncertain dynamics such that asymptotic convergence of the follower agents' states to the dynamic convex hull formed by the leaders' time-varying states is achieved. Simulation results are provided to demonstrate the effectiveness of the developed controller. Copyright © 2016 John Wiley & Sons, Ltd.

It is well known that multi-input, multi-output nature of nonlinear system and generalized exosystem have posed some challenges to output regulation theory. Recently, the global robust output regulation problem for a class of multivariable nonlinear system subject to a linear neutrally stable exosystem has been studied. It has been shown that a linear internal model-based state feedback control law can lead to the solution of previous problem. In this paper, we will further study the global robust output regulation problem of the system subject to a nonlinear exosystem. By utilizing nonlinear internal model design and decomposing the multi-input control problem into several single-input control problems, we will solve the problem by recursive control law design. The theoretical result is applied to the non-harmonic load torque disturbance rejection problem of a surface-mounted permanent magnet synchronous motor. Copyright © 2016 John Wiley & Sons, Ltd.

This paper deals with the high-precision consensus seeking problem of multi-agent systems when they are subject to switching topologies and varying communication time-delays. By combining the iterative learning control (ILC) approach, a distributed consensus seeking algorithm is presented based on only the relative information between every agent and its local (or nearest) neighbors. All agents can be enabled to achieve consensus exactly on a common output trajectory over a finite time interval. Furthermore, conditions are proposed to guarantee both exponential convergence and monotonic convergence for the resulting ILC processes of multi-agent consensus systems. In particular, the linear matrix inequality technique is employed to formulate the established convergence conditions, which can directly give formulas for the gain matrix design. An illustrative example is included to validate the effectiveness of the proposed ILC-motivated consensus seeking algorithm. Copyright © 2016 John Wiley & Sons, Ltd.

A new online iterative algorithm for solving the *H*_{∞} control problem of continuous-time Markovian jumping linear systems is developed. For comparison, an available offline iterative algorithm for converging to the solution of the *H*_{∞} control problem is firstly proposed. Based on the offline iterative algorithm and a new online decoupling technique named *subsystems transformation* method, a set of linear subsystems, which implementation in parallel, are obtained. By means of the adaptive dynamic programming technique, the two-player zero-sum game with the coupled game algebraic Riccati equation is solved online thereafter. The convergence of the novel policy iteration algorithm is also established. At last, simulation results have illustrated the effectiveness and applicability of these two methods. Copyright © 2016 John Wiley & Sons, Ltd.

We consider classical estimators for a class of physically realizable linear quantum systems. Optimal estimation using a complex Kalman filter for this problem has been previously explored. Here, we study robust *H*_{∞} estimation for uncertain linear quantum systems. The estimation problem is solved by converting it to a suitably scaled *H*_{∞} control problem. The solution is obtained in the form of two algebraic Riccati equations. Relevant examples involving dynamic squeezers are presented to illustrate the efficacy of our method. Copyright © 2016 John Wiley & Sons, Ltd.

This paper is concerned with the fault estimation for a class of discrete-time switched nonlinear systems with mixed time delays. The fault existing in the system is assumed to be characterized by an external system, which incorporates the fault's prior knowledge to the considered systems. The fault estimator is designed by using the multiple Lyapunov–Krasovskii functional and average dwell-time approach. Sufficient conditions in the form of linear matrix inequalities (LMIs) are developed to ensure the resulting error system is exponentially stable with an optimized disturbance attenuation level. The gain matrices of the estimator can be easily determined by using the standard optimization toolboxes. Finally, numerical examples and simulation results with the help of real-time systems are given to illustrate the effectiveness and advantages of the obtained results. Copyright © 2016 John Wiley & Sons, Ltd.

This note proposes the use of a tuple encoding scheme to reduce the number of binary variables involved in trajectory optimization problems with inter-sample avoidance constraints. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, the adaptive control problem of nonlinear teleoperation system based on the point of view of state-independent input-to-output stability is addressed. By intentionally introducing the switched filter systems, a new IOS-based control framework based on subsystem decomposition is developed. By designing the proper nonlinear controller, the complete closed-loop system is first modeled into two interconnected subsystems with some well-defined auxiliary variables. Then utilizing the small gain theorem, the weakly state-independent input-to-output stability of complete system can be derived by the stability of each subsystem. As an important extension, the proposed control scheme is also proved to be suitable for the control of the single-master-multi-slave teleoperation systems. Finally, the numerical example is given to demonstrate the effectiveness. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we consider the recursive state estimation problem for a class of discrete-time nonlinear systems with event-triggered data transmission, norm-bounded uncertainties, and multiple missing measurements. The phenomenon of event-triggered communication mechanism occurs only when the specified event-triggering condition is violated, which leads to a reduction in the number of excessive signal transmissions in a network. A sequence of independent Bernoulli random variables is employed to model the multiple measurements missing in the transmission. The norm-bounded uncertainties that could be considered as external disturbances which lie in a bounded set. The purpose of the addressed filtering problem is to obtain an optimal robust recursive filter in the minimum-variance sense such that with the simultaneous presence of event-triggered data transmission, norm-bounded uncertainties, and multiple missing measurements; the filtering error is minimized at each sampling time. By solving two Riccati-like difference equations, the filter gain is calculated recursively. Based on the stochastic analysis theory, it is proved that the estimation error is bounded under certain conditions. Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed algorithm. Copyright © 2016 John Wiley & Sons, Ltd.

The problem of global stabilization by output feedback is investigated in this paper for a class of nonminimum-phase nonlinear systems. The system under consideration has a cascade configuration that consists of a driven system known as the inverse dynamics and a driving system. It is proved that although the zero dynamics may be unstable, there is an output feedback controller, globally stabilizing the nonminimum-phase system if both driven and driving systems have a lower-triangular form and satisfy a Lipschitz-like condition, and the inverse dynamics satisfy a stronger version of input-to-state stabilizability condition. A design procedure is provided for the construction of an *n*-dimensional dynamic output feedback compensator. Examples and simulations are also given to validate the effectiveness of the proposed output feedback controller. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we investigate the problems of stabilization of networked control systems with quantization and actuator saturation via delta operator approach. The definition of the domain of attraction for delta operator systems is introduced to analyze the stochastic stability of the closed-loop networked control systems. The quantizer is a uniform one with arbitrary quantization regions, and the packet dropout process is modeled as a Bernoulli process. On the basis of the zoom strategy and Lyapunov theory in delta domain, sufficient conditions are given for the closed-loop delta operator systems to be mean square stable, and the feedback controllers are designed to ensure the stability of networked control systems. A single link direct joint driven manipulator model is presented to show the effectiveness of the main results. Copyright © 2016 John Wiley & Sons, Ltd.

This paper is concerned with the variance-constrained state estimation problem for a class of networked multi-rate systems (NMSs) with network-induced probabilistic sensor failures and measurement quantization. The stochastic characteristics of the sensor failures are governed by mutually independent random variables over the interval [0,1]. By applying the lifting technique, an augmented system model is established to facilitate the state estimation of the underlying NMSs. With the aid of the stochastic analysis approach, sufficient conditions are derived under which the exponential mean-square stability of the augmented system is guaranteed, the prescribed *H*_{∞} performance constraint is achieved, and the individual variance constraint on the steady-state estimation error is satisfied. Based on the derived conditions, the addressed variance-constrained state estimation problem of NMSs is recast as a convex optimization one that can be solved via the semi-definite program method. Furthermore, the explicit expression of the desired estimator gains is obtained by means of the feasibility of certain matrix inequalities. Two additional optimization problems are considered with respect to the *H*_{∞} performance index and the weighted error variances. Finally, a simulation example is utilized to illustrate the effectiveness of the proposed state estimation method. Copyright © 2016 John Wiley & Sons, Ltd.

Fault-tolerant control systems are vital in many industrial systems. Actuator redundancy is employed in advanced control strategies to increase system maneuverability, flexibility, safety, and fault tolerability. Management of control signals among redundant actuators is the task of control allocation algorithms. Simplicity, accuracy and low computational cost are key issues in control allocation implementations. In this paper, an adaptive control allocation method based on the pseudo inverse along the null space of the control matrix (PAN) is introduced in order to adaptively tolerate actuator faults. The proposed method solves the control allocation problem with an exact solution and optimized *l*_{∞} norm of the control signal. This method also handles input limitations and is computationally efficient. Simulation results are used to show the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.

A novel anti-windup design method is provided for a class of uncertain nonlinear systems subject to actuator saturation and external disturbance. The controller considered incorporates both an active disturbance rejection controller as well as an anti-windup compensator. The dynamical uncertainties and external disturbance are treated as an extended state of the plant, and then estimate it using an extended state observer and compensate for it in the control action, in real time. The anti-windup compensator produces a signal based on the difference between the controller output and the saturated actuator output, and then augment the signal to the control to deal with the windup phenomenon caused by actuator saturation. We first show that, with the application of the proposed controller, the considered nonlinear system is asymptotically stable in a region including the origin. Then, in the case that the controller in linear form, we establish a linear matrix inequality-based framework to compute the extended state observer gain and the anti-windup compensation gain that maximize the estimate of the domain of attraction of the resulting closed-loop system. The effectiveness of the proposed method is illustrated by a numerical example. Copyright © 2016 John Wiley & Sons, Ltd.

This paper considers the robustness of a feedback connection of a known linear parameter varying system and a perturbation. A sufficient condition is derived to bound the worst-case gain and ensure robust asymptotic stability. The input/output behavior of the perturbation is described by multiple integral quadratic constraints (IQCs). The analysis condition is formulated as a dissipation inequality. The standard approach requires a non-negative definite storage function and the use of ‘hard’ IQCs. The term ‘hard’ means that the IQCs can be specified as time-domain integral constraints that hold over all finite horizons. The main result demonstrates that the dissipation inequality condition can be formulated requiring neither a non-negative storage function nor hard IQCs. A key insight used to prove this result is that the multiple IQCs, when combined, contain hidden stored energy. This result can lead to less conservative robustness bounds. Two simple examples are presented to demonstrate this fact. Copyright © 2016 John Wiley & Sons, Ltd.

This paper considers both semi-global and global containment control for a second-order multi-agent system that is composed by a network of identical harmonic oscillators or double integrators with multiple leaders and input saturation. A distributed low gain feedback algorithm is proposed to solve the semi-global containment control problem for the network whose topology is directed and initial condition is taken from any a priori given bounded set. In particular, by using a parametric Lyapunov equation approach, *M*-matrix properties and algebraic graph theory, an upper bound of the low gain parameter is estimated such that the low gain feedback matrix can be analytically determined without involving numerical computation. Furthermore, under the assumption that the induced subgraph formed by the followers is strongly connected and detail balanced, two linear feedback protocols are designed for coupled harmonic oscillators and coupled double integrators, respectively, to asymptotically achieve the global containment control of the network with any initial condition. Finally, numerical examples are given to illustrate the effectiveness of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.

This paper is concentrated on the problem of fault estimation for a class of linear systems with partially dynamic uncertainty and actuator faults. A novel input–output-based fault estimation approach is proposed, by which the estimates can asymptotically converge to the magnitudes of the actuator faults, and the asymptotic convergence of the estimation is theoretically proved. Some important properties related to the corresponding fault errors are obtained. The proposed input–output-based fault estimation method can exponentially weaken the effects of the fault derivatives on the fault error dynamics. Based on the online estimates, a corresponding robust fault-tolerant control policy is designed, so that the closed-loop system is asymptotically stable and the control output curves can asymptotically trace to the normal control output curves. Finally, three examples are given to show the effectiveness, merits, and applications of the proposed methods. Copyright © 2016 John Wiley & Sons, Ltd.

Time-varying output formation control problems for linear multi-agent systems with switching topologies are studied, where two types of switching topologies are considered: (1) the topology is undirected and jointly connected, and 2) each topology is directed and has a spanning tree. An output formation protocol under switching topologies is constructed using the outputs of neighboring agents via dynamic output feedback. Two algorithms are proposed to design the dynamic protocols under both jointly connected topologies and switching directed topologies. Time-varying output formation feasibility conditions are given to describe the compatible relationship among the desired time-varying output formation, the dynamics of each agent, and the switching topologies. The stability of the closed-loop multi-agent systems under the proposed two algorithms is investigated based on the common Lyapunov functional theory and the piecewise Lyapunov functional theory, respectively. In the case where the topologies are jointly connected, time-varying output formation can be achieved for multi-agent systems using the designed protocol if the given time-varying output formation satisfies the feasible constraint. For the case where the switching topologies are directed and have a spanning tree, the time-varying output formation can be realized if the output formation feasibility constraint is satisfied and the dwell time is larger than a positive threshold. Moreover, approaches to determine the output formation references are provided to describe the macroscopic movement of the time-varying output formation. Finally, numerical simulation results are presented to demonstrate the effectiveness of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.

This paper focuses on stabilization on null controllable region of delta operator systems subject to actuator saturation via constructing suitable controllers. Under a saturated linear feedback law, a set of stable equilibrium points is obtained for the delta operator system with actuator saturation. A comprehensive controller is given to show global stabilization of the delta operator system. Thereby, semi-global stabilization of the delta operator system is also achieved. For higher-order systems with no more than two unstable exponentially poles, a new feedback law is constructed to achieve semi-global stabilization on the null controllable region. Finally, three examples are given to illustrate the effectiveness of the proposed techniques. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we consider the control problem of strict-feedback nonlinear systems with time-varying input and output delays. The approach is based on the usual observer/predictor/feedback approach, but the novelty is the use of the closed-loop dynamics in the predictor. This approach allows to develop two designs, an instantaneous predictor and a delay differential equation-based predictor, that both attain the same performance in terms of system trajectories and input signal as in the case with no delays. The design based on delay differential equations allows to build a cascade of predictors to deal with arbitrarily large delay bounds. The resulting controller is much simpler to implement than classical infinite-dimensional predictors, and it is robust with respect to actuation and measurement disturbances. We illustrate the approach with an application to the control of a chaotic system with input delay. Copyright © 2016 John Wiley & Sons, Ltd.

This paper proposes modified static anti-windup techniques for saturated systems with sector-bounded and slope-restricted nonlinearities by augmenting the pre-designed controller with the so-called differential compensator to process the slope restriction. By using a purely quadratic Lyapunov function and with a modified sector condition dealing with actuator saturation, LMI-based synthesis conditions are presented to address the problems of the estimates of the region of attraction and performance analysis of the closed-loop system. Numerical examples illustrate the effectiveness of the proposed approaches. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, a consensus problem is studied for a group of second-order nonlinear heterogeneous agents with non-uniform time delay in communication links and uncertainty in agent dynamics. We design a class of novel decentralized control protocols for the consensus problem whose solvability is converted into stability analysis of an associated closed-loop system with uncertainty and time delay. Using an explicitly constructed Lyapunov functional, the stability conditions or the solvability conditions of the consensus problem are given in terms of a set of linear matrix inequalities apart from a small number of scalar parameters that appear nonlinearly. Furthermore, the linear matrix inequalities are theoretically verified to be solvable when the communication delay is sufficiently small. The effectiveness of the proposed control protocol is illustrated by numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.

This paper proposes a consensus protocol for a class of high-order multiagent systems under directed networks. It is supposed that each agent is exposed to an external disturbance additive to its control input. Based on the optimization theory, the consensus protocol gains are designed in order to attenuate the effects of the external disturbances on the performance of the multiagent system. The main problem of existing high-order consensus protocols in the literature is the dependency of the design on the information of coupling matrices associated with networks topologies. Despite existing high-order consensus protocols in the literature, the proposed consensus protocol can be designed in a fully decentralized manner based on no global information. The main idea of the design is to propose an control formulation in which the coupling information of the agents is considered as exogenous signals, while the coupling effects of these signals lead to achieving consensus in the multiagent system. Numerical examples verify the effectiveness of the proposed consensus protocol. Copyright © 2016 John Wiley & Sons, Ltd.

This paper addresses the problems of stability analysis and stabilization of sampled-data control systems under magnitude and rate saturating actuators. A position-type feedback modeling for the actuator is considered. Based on the use of a quadratic Lyapunov function, a looped-functional, and generalized sector relations (to cope with nested saturation functions), LMI-based conditions are derived to assess local (regional) and global stability of the closed-loop systems under aperiodic sampling strategies and also to synthesize stabilizing sampled-data state feedback control laws. These conditions are then incorporated in convex optimization problems aiming at maximizing estimates of the region of attraction of the origin or maximizing the inter-sampling time for which the stability is ensured regionally or, when possible, globally. Copyright © 2016 John Wiley & Sons, Ltd.

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]]>A robust fault-tolerant control scheme is proposed for uncertain nonlinear systems with zero dynamics, affected by actuator faults and lock-in-place and float failures. The proposed controller utilizes an adaptive second-order sliding mode strategy integrated with the backstepping procedure, retaining the benefits of both the methodologies. A Lyapunov stability analysis has been conducted, which unfolds the advantages offered by the proposed methodology in the presence of inherent modeling errors and strong eventualities of faults and failures. Two modified adaptive laws have been formulated, to approximate the bounds of uncertainties due to modeling and to estimate the fault-induced parametric uncertainties. The proposed scheme ensures robustness towards linearly parameterized mismatched uncertainties, in addition to parametric and nonparametric matched perturbations. The proposed controller has been shown to yield an improved post-fault transient performance without any additional expense in the control energy spent. The proposed scheme is applied to the pitch control problem of a nonlinear longitudinal model of Boeing 747-100/200 aircraft. Simulation results support theoretical propositions and confirm that the proposed controller produces superior post-fault transient performance compared with already existing approaches designed for similar applications. Besides, the asymptotic stability of the overall controlled system is also established in the event of such faults and failures. Copyright © 2015 John Wiley & Sons, Ltd.

Robust *λ*-contractive sets have been proposed in previous literature for uncertain polytopic linear systems. It is well known that, if initial state is inside such sets, it is guaranteed to converge to the origin. This work presents the generalization of such concepts to systems whose behaviour changes among different linear models with probability given by a Markov chain. We propose sequence-dependent sets and associated controllers that can ensure a reliability bound when initial conditions are outside the maximal *λ*-contractive set. Such reliability bound will be understood as the probability of actually reaching the origin from a given initial condition without violating constraints. As initial conditions are further away from the origin, the likelihood of reaching the origin decreases. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, an observer-based control approach is proposed for uncertain stochastic nonlinear discrete-time systems with input constraints. The widely used extended Kalman filter (EKF) is well known to be inadequate for estimating the states of uncertain nonlinear dynamical systems with strong nonlinearities especially if the time horizon of the estimation process is relatively long. Instead, a modified version of the EKF with improved stability and robustness is proposed for estimating the states of such systems. A constrained observer-based controller is then developed using the state-dependent Riccati equation approach. Rigorous analysis of the stability of the developed stochastically controlled system is presented. The developed approach is applied to control the performance of a synchronous generator connected to an infinite bus and chaos in permanent magnet synchronous motor. Simulation results of the synchronous generator show that the estimated states resulting from the proposed estimator are stable, whereas those resulting from the EKF diverge. Moreover, satisfactory performance is achieved by applying the developed observer-based control strategy on the two practical problems. Copyright © 2015 John Wiley & Sons, Ltd.

This paper presents a new perspective on the stability problem for uncertain LTI feedback systems with actuator input amplitude saturation. The solution is obtained using the quantitative feedback theory and a 3 DoF non-interfering control structure. Describing function (DF) analysis is used as a criterion for closed loop stability and limit cycle avoidance, but the circle or Popov criteria could also be employed. The novelty is the combination of a controller parameterization from the literature and describing function-based limit cycle avoidance with margins for uncertain plants. Two examples are given. The first is a benchmark problem and a comparison is made with other proposed solutions. The second is an example that was implemented and tested on an X-Y linear stage used for nano-positioning applications. Design and implementation considerations are given. An example is given on how the method can be extended to amplitude and rate saturation with the help of the generalized describing function, and a novel anti-windup compensation structure inspired by previous contributions. Copyright © 2015 John Wiley & Sons, Ltd.

This paper investigates the finite-time stabilization of a class of switched stochastic nonlinear systems under arbitrary switching, where each subsystem has a chained integrator with the power *r* (0 < *r* < 1). By using the technique of adding a power integrator, a continuous state-feedback controller is constructed, and it is proved that the solution of the closed-loop system is finite-time stable in probability. Two simulation examples are provided to show the effectiveness of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.

This paper is concerned with the problem of seeking consensus for a network of agents under a fixed or switching directed communication topology. Each agent is modeled as discrete-time first-order dynamics and interacts with its neighbors via logarithmically quantized information. We assume that the digraph is not necessarily balanced and, thus, avoiding the double stochasticity requirement for the adjacency matrix. For the case of a fixed topology that is strongly connected, it is shown that the proposed protocol is admissible for arbitrarily coarse logarithmic quantization and the *β*-asymptotic weighted-average consensus is achieved. For the case of a switching topology that is periodically strongly connected, it is shown that the proposed protocol is admissible for arbitrarily coarse quantization and the *β*-asymptotic consensus is achieved. Furthermore, for both cases, not only are the convergence rates for consensus specified but also the bounds on the consensus error that highlight their dependence on the sector bound *β* of the logarithmic quantizer are also provided. Copyright © 2015 John Wiley & Sons, Ltd.

This paper aims to develop the stability theory for singular stochastic Markov jump systems with state-dependent noise, including both continuous-time and discrete-time cases. The sufficient conditions for the existence and uniqueness of a solution to the system equation are provided. Some new and fundamental concepts such as non-impulsiveness and mean square admissibility are introduced, which are different from those of other existing works. By making use of the
-representation technique and the pseudo inverse *E*^{+} of a singular matrix *E*, sufficient conditions ensuring the system to be mean square admissible are established in terms of strict linear matrix inequalities, which can be regarded as extensions of the corresponding results of deterministic singular systems and normal stochastic systems. Practical examples are given to demonstrate the effectiveness of the proposed approaches. Copyright © 2015 John Wiley & Sons, Ltd.

We investigate the problem of robust adaptive tracking by output feedback for a class of uncertain nonlinear systems. Based on the high-gain scaling technique and a new adaptive law, a linear-like output feedback controller is constructed. Only one dynamic gain is designed, which makes the controller easier to implement. Furthermore, by modifying the update law, the adaptive controller is robust to bounded external disturbance and is able to guarantee the convergence of the output tracking error to an arbitrarily small residual set. A numerical example is used to illustrate the effectiveness of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.

This paper addresses the problem of almost disturbance decoupling (ADD) using sampled-data output feedback control for a class of continuous-time nonlinear systems. Under a lower-triangular linear growth condition, a sampled-data output feedback controller is constructed based on the output feedback domination approach, and a Gronwall–Bellman-like inequality is established in the presence of disturbances. Even though a sampled-data controller is employed for easy computer implementation, the proposed controller is still able to achieve ADD under the commonly used continuous-time requirement, that is, the disturbances' effect on the output is attenuated to an arbitrary degree of accuracy in the *L*_{2} gain sense. Copyright © 2015 John Wiley & Sons, Ltd.

This paper deals with the problem of control of partially known nonlinear systems, which have an open-loop stable equilibrium, but we would like to add a PI controller to regulate its behavior around another operating point. Our main contribution is the identification of a class of systems for which a globally stable PI can be designed knowing only the systems input matrix and measuring only the actuated coordinates. The construction of the PI is carried out invoking passivity theory. The difficulties encountered in the design of adaptive PI controllers with the existing theoretical tools are also discussed. As an illustration of the theory, we consider a class of thermal processes. Copyright © 2015 John Wiley & Sons, Ltd.

The stability of uncertain periodic and pseudo-periodic systems with impulses is analyzed in the looped-functional and clock-dependent Lyapunov function frameworks. These alternative and equivalent ways for characterizing discrete-time stability have the benefit of leading to stability conditions that are convex in the system matrices, hence suitable for robust stability analysis. These approaches, therefore, circumvent the problem of computing the monodromy matrix associated with the system, which is known to be a major difficulty when the system is uncertain. Convex stabilization conditions using a non-restrictive class of state-feedback controllers are also provided. The obtained results readily extend to uncertain impulsive periodic and pseudo-periodic systems, a generalization of periodic systems that admit changes in the ‘period’ from one pseudo-period to another. The obtained conditions are expressed as infinite-dimensional semidefinite programs, which can be solved using recent polynomial programming techniques. Several examples illustrate the approach, and comparative discussions between the different approaches are provided. A major result obtained in the paper is that despite being equivalent, the approach based on looped functional reduces to the one based on clock-dependent Lyapunov functions when a particular structure for the looped functional is considered. The conclusion is that the approach based on clock-dependent Lyapunov functions is preferable because of its lower computational complexity and its convenient structure enabling control design. Copyright © 2015 John Wiley & Sons, Ltd.

This paper addresses output regulation of heterogeneous linear multi-agent systems. We first show that output regulation can be achieved through local controller design, then we formulate output regulation in the graphical game framework. To solve output regulation of heterogeneous linear multi-agent system in the graphical game framework, one needs to derive a solution to the coupled Hamilton–Jacobi equations. Both offline and online algorithms are suggested for that solution. Using the online method, the profile policy converges to a Nash Equilibrium. Besides, it is shown that the graphical formulation is robust to the multiplicative uncertainty satisfying an upper bound and it has an infinite gain margin. Copyright © 2015 John Wiley & Sons, Ltd.