Robust exponential l2 − l ∞  control for discrete-time switched system: A cone complement linearization method


Guangdeng Zong, Institute of Automation, Qufu Normal University, Qufu 273165, Shandong, China.



The robust exponential l2 − l ∞  control problem is considered in this paper for discrete-time switched systems with both time-varying delay and norm-bounded parameter uncertainties. An exponential l2 − l ∞  performance index is first introduced for the discrete-time switched systems. The designed controller is a memory exponential l2 − l ∞  controller. By introducing an average dwell time approach and a Lyapunov–Krasovskii functional technique, some sufficient criteria guaranteeing exponential stability are presented, and the desired memory exponential l2 − l ∞  controller is established by resorting to a cone complement linearization method. Some results on exponential stability using memoryless exponential l2 − l ∞  controller and asymptotical stability with traditional l2 − l ∞  performance index are also established. Finally, a numerical example is provided to demonstrate that the proposed approach can lead to less conservatism compared with the developed result using memoryless exponential l2 − l ∞  controller and asymptotical stability analysis with traditional l2 − l ∞  performance index. Copyright © 2011 John Wiley & Sons, Ltd.