Global synchronization of dynamical networks with time delay

In this paper, we consider the global asymptotic synchronization of a class of dynamical networks whose nodes are identical nonlinear systems interconnected by both delay free and time delay couplings. Two different outer coupling matrices are used to represent these coupling terms, and are not required to be simultaneously diagonalizable which is too restrictive in practice. Based on the Lyapunov-Krasovskii functional method, two sufficient delay-dependent conditions are obtained in terms of N - 1 linear matrix inequalities (LMIs) under which the global asymptotic synchronization of such a network is achieved. A dynamical network consisting of modified Chua's circuit is simulated to demonstrate the effectiveness of the theoretical results.