Synchronization of complex dynamical networks with switching topology: A switched system point of view

Abstract: In this paper, we study the synchronization problem for complex dynamical networks with switching topology. The synchronization problem is transformed into the stability problem for a time-varying switched system. We address two basic problems: synchronization under arbitrary switching topology, and synchronization via design of switching within a pre-given collection of topologies when synchronization can not be achieved by using any topology alone in this collection. For the both problems, we first establish synchronization criteria for general connection topology. Then, under the condition of simultaneous triangularization of the connection matrices, a common Lyapunov function and a single Lyapunov function are systematically constructed respectively by those of several lower-dimensional dynamic systems.