Pinning Synchronization for a General Complex Networks with Multiple Time-Varying Coupling Delays

This paper investigates the problem of pinning synchronization for a general complex networks with multiple time-varying coupling delays by using Lyapunov functional method. Firstly, we design a controller to keep the given system synchronized, and provide a simple approximate formula to estimate the detailed pinning synchronization states. Furthermore, by using the same method, an adaptive pinning control scheme is developed to achieve global synchronization, and the adaptive pinning controllers are simpler than some traditional controllers. Moreover, the presented results can also be applied to the system with single time delay, and the coupling-configuration matrices are not necessarily symmetric. Finally, numerical examples are given to show the effectiveness of the proposed methods.