On Pinning Synchronization of An Array of Linearly Coupled Dynamical Network

Abstract

In this paper, we investigate the exponential synchronization problem for a class of linear coupled dynamic complex networks. In a complex network system, it is difficult to achieve synchronization only by the coupling of the network itself without the controller. Based on the linear feedback method, this paper proposes a strategy to achieve global exponential stability of the general complex dynamic network in the target state by means of pinning control. Some nodes of the complex network are controlled to achieve the same state of all nodes of the complex network. In addition, the conditions of global exponential synchronization of the complex network are given, and the strict proof is given by using Lyapunov stability theory. Numerical analysis and simulation results are presented to demonstrate effectiveness of the criterion.