Cluster exponential synchronization of a class of complex networks with hybrid coupling and time-varying delay

This paper deals with the cluster exponential synchronization of a class of complex networks with hybrid coupling and time-varying delay. Through constructing an appropriate Lyapunov—Krasovskii functional and applying the theory of the Kronecker product of matrices and the linear matrix inequality (LMI) technique, several novel sufficient conditions for cluster exponential synchronization are obtained. These cluster exponential synchronization conditions adopt the bounds of both time delay and its derivative, which are less conservative. Finally, the numerical simulations are performed to show the effectiveness of the theoretical results. (general)