Exponentially asymptotic synchronization of uncertain complex time-delay dynamical networks

This paper investigates the problem of exponentially asymptotic synchronization of complex time-delay dynamical networks with multi-links and structure uncertainty. The structure uncertainty belongs to the uncertain coupling strength and unknown topologies structures, which appear typically in networks environment. In order to synchronize complex networks with structure uncertainty, the adaptive controller is designed, and some general synchronization criteria of the controllers are proposed and proved based on the Lyapunov stability theory and the Lipschitz hypothesis. Finally, numerical simulations of dynamical networks with different topological structures are presented to demonstrate the feasibility and the effectiveness of the results.