Event-triggered exponential synchronization of complex dynamical networks with cooperatively directed spanning tree topology

Abstract

This paper focuses on the exponential synchronization problem of complex dynamical networks (CDNs) with time-varying network topology via event-triggered communication strategy. The definition of a new time-varying network topology, called cooperatively directed spanning tree topology, is first given based on the integral of time-varying Laplacian matrix. This topology does not require the network constantly connected. In other words, the network topology is allowed to be disconnected at all times, but only the integral of the Laplacian matrix of the network graph is required to contain directed spanning tree over a period of time. Moreover, in order to achieve the exponential synchronization for CDNs under the cooperatively directed spanning tree topology, a sufficient condition is derived by the virtues of algebraic graph theory, event-triggered communication strategy, matrix inequality and the special Lyapunov stability analysis method. Additionally, event-triggered communication strategy can avoid continuous communication, which can reduce the communication load and energy consumption. The Zeno behavior is excluded as well by the strictly positive sampling intervals based on the upper right-hand Dini derivative, and thus to avoid infinite triggers. Finally, simulation examples are given to show the effectiveness of the proposed exponential synchronization criteria.