Synchronization for complex dynamical networks with mixed mode-dependent time delays

In this paper, the problem of synchronization control is investigated for complex dynamical networks with discrete intervals and distributed time-varying delays. The main thing is to design a properly pinning controller, for which the error system of complex dynamical networks is asymptotically stable. Based on the theory of Lyapunov stability and linear matrix inequality, the suitable Lyapunov-Krasovskii functional is constructed in terms of the Kronecker product, and then we obtain a novel synchronization criterion. Finally, a numerical example is given to illustrate the effectiveness of the proposed methods.