Pinning adaptive and impulsive synchronization of fractional-order complex dynamical networks

This paper is concerned with the pinning adaptive and impulsive synchronization problem of fractional-order complex dynamical networks. First, a generalized Barbalat's Lemma is derived. Based on the generalized Barbalat's Lemma and some analysis techniques, we obtain some criteria, which guarantee that the whole state-coupled dynamical network can be forced to certain desired synchronous state by combining pinning adaptive control and pinning impulsive control. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed control strategy.