Abstract

The synchronization problem for complex dynamical networks with Markov switching is studied in this paper. Two kinds of directed network topology are considered: (i) strongly connected networks and (ii) networks containing a directed spanning tree. By the ergodic theory of continuous time Markov chain, together with Lyapunov function method, some almost surely exponential synchronization criteria are derived to show that although subsystems may not be synchronized, the overall system can achieve exponential synchronization almost surely. In view of environmental noise, we also discuss exponential synchronization in mean square for stochastic coupled networks with switching by |$M$|-matrix method. In addition, some examples with numerical simulations are given to illustrate the theoretical results.

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