On synchronizability of nonlinear networked systems with the switching topology and with the unit inner-coupling matrix

The synchronizability 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 an unit matrix. The critical idea is to convert the synchronization problem to the 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 over 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.