Abstract
•Compared with [13,16,30], the time delay is considered on the impulse. Hence, the corresponding main theorems of FTS of CDNs in this paper extend the results of previous related works. In addition, the effects of synchronizing and desynchronizing impulses on the FTS of the CDNs are considered, respectively.•In contrast to [17,21], the initial value constraint has been removed. The GFTS criteria of CDNs with delayed impulses are derived under synchronizing impulses. Furthermore, a larger settling time bound is estimated when CDNs are subjected to desynchronizing impulses in Theorem 2.
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.