Cluster synchronization of complex networks via event-triggered strategy under stochastic sampling

•Mean square cluster synchronization in directed networks is studied.•The interacting nodes communicate with each other at stochastic periods.•An event-triggered scheme is proposed based on the sampled-data.•Virtual leader is supposed to apply pinning control to following nodes.

This paper is concerned with the issue of mean square cluster synchronization of non-identical nodes connected by a directed network. Suppose that the nodes possess nonlinear dynamics and split into several clusters, then an event-triggered control scheme is proposed for synchronization based on the information from stochastic sampling. Meanwhile, an equilibrium is considered to be the synchronization state or the virtual leader for each cluster, which can apply pinning control to the following nodes. Assume that a spanning tree exists in the subgraph consisting of the nodes belonging to the same cluster and the corresponding virtual leader, and the instants for updating controllers are determined by the given event-triggered strategy, then some sufficient conditions for cluster synchronization are presented according to the Lyapunov stability theory and linear matrix inequality technique. Finally, a specific numerical example is shown to demonstrate the effectiveness of the theoretical results.