Analysis and adaptive control for robust synchronization and H_∞ synchronization of complex dynamical networks with multiple time-delays

In this paper, the robust synchronization and robust H_∞ synchronization for complex networks with multiple time-delays are respectively investigated. Firstly, the robust synchronization for the complex network with multiple time-delays is analyzed by using inequality techniques and constructing appropriate Lyapunov functional. Then, an adaptive controller is designed to ensure the robust synchronization for such network. Moreover, considering the most of networks exist external disturbances, we also analyze the robust H_∞ synchronization of complex networks with multiple time-delays, and an adaptive controller is developed to guarantee the robust H_∞ synchronization for such network. Finally, in order to verify the validity of these acquired results, two numerical examples are provided.