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Proportional-delay adaptive control for global synchronization of complex networks with time-delay and switching outer-coupling matrices


Correspondence to: Tianbo Wang, College of Information Sciences and Technology, Donghua University, Shanghai 200051, China.



In this paper, the global synchronization problem for complex dynamical networks with time-delay and switching outer-coupling matrices is studied using the method of adaptive control. The mixed time-delays in the considered system comprise both discrete time-varying delay and distributed delay. The outer-coupling matrices in the complex networks are assumed to vary with time and are described by a Markov process with finite state values. Based on the Lyapunov stability theory, the complete-square method, and the Kronecker product analysis technique, a sufficient condition, which guarantees the global synchronization of all of nodes is obtained. The updated laws of controller do not only depend on the lag states of the complex dynamical networks but also depend on the Markov process. Finally, a numerical example is provided to show the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.