Synchronization of complex networks with PID pinning controller

Recently, synchronization of complex networks has been studied deeply; however, most existing works take the standard proportional control strategy approach to pinning controllers, which produces a steady-state error and has a significant time of fluctuation. In order to solve this problem, we propose a new method using the Proportional-Integral-Differential (PID) control to design a pinning control method for synchronization of complex networks. Based on Lyapunov theory, the stability of the network is proved, and sufficient synchronization conditions are obtained. Finally, examples are given to evaluate the effectiveness of the proposed PID pinning method and compare it to the traditional proportional pinning controller and adaptive pinning controller.