A General Complex Dynamical Network With Time-Varying Delays and Its Novel Controlled Synchronization Criteria

In this paper, a general complex dynamical network with time-varying delays is introduced. Then, the synchronization problem of the complex dynamical network is further investigated. Most studies make use of linear matrix inequalities (LMIs) to obtain synchronization criteria. However, it is difficult to construct the Lyapunov function using LMIs. To avoid constructing the Lyapunov function, the stability of the synchronization state is investigated based on the theory of the asymptotic stability of linear time-delay systems in this paper. Then, we have obtained two new general stability criteria of the synchronization state in complex dynamical networks in light of the stability theory of the linear time-delay system. Hence, these criteria are easy to be verified. Moreover, these synchronization conditions are applicable to networks with different topologies and sizes. In the end, numerical simulations are provided to verify the effectiveness and feasibility of the developed theorems.