Global Phase Synchronization for a Class of Dynamical Complex Networks with Time-Varying Coupling Delays

Global phase synchronization for a class of dynamical complex networks composed of multiinput multioutput pendulum-like systems with time-varying coupling delays is investigated. The problem of the global phase synchronization for the complex networks is equivalent to the problem of the asymptotical stability for the corresponding error dynamical networks. For reducing the conservation, no linearization technique is involved, but by Kronecker product, the problem of the asymptotical stability of the high dimensional error dynamical networks is reduced to the same problem of a class of low dimensional error systems. The delay-dependent criteria guaranteeing global asymptotical stability for the error dynamical complex networks in terms of Liner Matrix Inequalities LMIs are derived based on free-weighting matrices technique and Lyapunov function. According to the convex characterization, a simple criterion is proposed. A numerical example is provided to demonstrate the effectiveness of the proposed results.