Finite-time synchronization of complex dynamical networks under delayed impulsive effects

Abstract

This paper mainly studies the finite-time synchronization (FTS) of complex dynamical networks (CDNs) with delayed impulses. By constructing proper Lyapunov function, some sufficient criteria for FTS of CDNs under synchronizing and desynchronizing impulses are established, respectively. Firstly, the existing results of FTS are extended to the case with delayed impulses. Secondly, when the impulses in the CDNs are synchronizing, the existing criterion of local FTS (LFTS) is extended to global FTS (GFTS) and the settling time which depends on the initial values and the impulses is estimated. Furthermore, the bound of settling time is estimated explicitly when the CDNs are subjected to desynchronizing impulses. Finally, three examples are given to illustrate the validity of the obtained results.