Global asymptotical synchronization of delayed complex dynamical networks with switching topology

In this paper, we study the global asymptotical synchronization problem of delayed complex dynamical networks with a pre-given collection of general connection topologies where synchronization cannot be achieved by using any topology alone in this collection. By using single Lyapunov and multiple Lyapunov function methods, two global asymptotical synchronization conditions with the design of switching within the pre-given collection of topologies are presented for synchronizing such complex dynamical networks. According to the topological structure of the connection matrices, we consider more general forms. Simultaneous triangularizability, diagonalizability or even symmetry of the connection matrices is no longer assumed. Finally, simulation results are used to demonstrate the effectiveness of the proposed results.