Synchronization of delayed dynamical networks with switching topologies

To reduce the conservativeness of switching signals introduced by a common average dwell-time condition, this paper uses the mode-dependent average dwell-time method to study the global exponential synchronization problem of a class of dynamical networks with switching topologies as well as time-varying coupling delays. First, we extend the mode-dependent average dwell-time method into the stability analysis of switched linear systems with time-varying delays. Then, we apply the obtained results to studying the synchronization problem of a particular network whose nodes have Lur´e type dynamics. A new delay-dependent sufficient condition is established in terms of linear matrix inequalities (LMIs) that guarantees the solvability of the problem, and a class of synchronizing switching signals, in which each subnetwork has its own average dwell-time scheme, is identified. Finally, a numerical example is given to show the effectiveness of the proposed results.