Leader-Following Pinning Synchronization of Multiagent Systems with Impulsive Interlayer Coupling

This article is mainly concerned with leader-following pinning synchronization of multiagent systems in a multiplex network setting, where the interlayer couplings are impulsive. The goal is to enforce all the followers to asymptotically synchronize with the leader via impulsive pinning control. Firstly, based on the Lyapunov stability theory of impulsive differential equations, some general synchronization criteria are derived. The synchronization index is then defined. We explore how the synchronization index is effected by major network parameters, including the impulse strength, the impulse interval, the pinning gain and the number of layers. In particular, with equivalent impulse intervals, when both the impulse strength and the pinning gain are constant, it is found that the least number of pinned nodes needed for achieving complete synchronization (CS) decreases with decreasing impulse intervals, whereas it firstly decreases and then increases with increasing impulse strength and pinning gain. Furthermore, the synchronization region enlarges as the impulse interval decreases, while narrows as the number of layers increases. Numerical simulations verify the correctness of these results.