Pinning impulsive synchronization of complex dynamical networks with various time-varying delay sizes

This paper studies the pinning impulsive synchronization problem for a class of complex dynamical networks with time-varying delay. By applying the Lyapunov stability theory and mathematical analysis technique, sufficient verifiable criterion for the synchronization of delayed complex dynamical networks with small delay is derived analytically. It is shown that synchronization can be achieved by only impulsively controlling a small fraction of network nodes. Moreover, a novel sufficient condition is constructed to relax the restrictions on the size of time-delay and guarantee the synchronization of concerned networks with large delay. Two numerical examples are presented to illustrate the effectiveness of the obtained results.