Cluster Synchronization of Complex Networks with Non-delayed and Delayed Coupling under Pinning Control

Abstract

In this paper, we focus on the cluster synchronization problem of a general network with non-delayed and delayed coupling. Based on the linear negative feedback control scheme, we use the Lyapunov stability theorem and linear matrix inequality (LMI) to obtain sufficient conditions which guarantee the realization of the cluster synchronization pattern for all initial values. Besides, numerical simulation is also given to support the validity of our theoretical results.