Pinning Synchronization of Directed Complex Dynamical Networks with Multi-links

Based on a method of network split through different nature of time-delay, this paper is further investigates the pinning synchronization of the directed complex dynamical networks with multi-links. Via the theory of Lyapunov stability combined with linear matrix inequalities (LMIs) technique and the method of the free-weighting matrix, some sufficient conditions for global synchronization by adding linear feedback controllers to a part of nodes are obtained. Numerical examples are also provided to demonstrate the effectiveness of the theory.