On local synchronisability of nonlinear networked systems with a unit inner-coupling matrix and switching topology

The local synchronization of the nonlinear networked systems with switching topology has been studied in this paper for the special case in which the inner coupling matrix is a unit matrix. The critical idea is to convert synchronization problem to consensus problem such that the switching topology can be dealt with effectively without any extra assumption on the relationship among the involved topologies. A novel local synchronous criterion consisting of the maximum Lyapunov exponent of nodal self-dynamics and the consensus convergent rate of the switching topology is given. To illustrate the effectiveness of the analytical results, two numerical examples on chaos synchronization are simulated respectively for the periodic switching case and randomly switching case.