Global Synchronization of General Complex Dynamical Networks with Time-Varying Delay

A new result of global synchronization for more general delay complex dynamical networks with time-varying delay is obtained in this paper. In this paper, based on an appropriate Lyapunov function, the sufficient condition for the global synchronization is given here by using the linear matrix inequality and introducing a reference state, and this condition is simply given based on the maximum nonzero eigenvalue of the network coupling matrix. Moreover, we give how to construct the coupling matrix to guarantee global synchronization of network, which is very convenient to use. A two-dimension system with time-varying delay as a dynamical node in network with global coupling is finally given, which is used to verify the theoretical results of the proposed global synchronization scheme.