Pinning outer synchronization of partially coupled dynamical networks with complex inner coupling matrices

This paper investigates outer synchronization of partially coupled dynamical networks with complex inner coupling matrices via pinning impulsive controller. At first, we establish more realistic drive-response partially coupled networks, where the inner coupling matrices between coupled nodes can be non-full rank and also asymmetric. Then, a weighted-norm-based method is given to select the nodes that should be pinning controlled, and our synchronization criteria derived by this method can be proved to be less conservative. By using the regrouping method and our new average impulsive interval method, some efficient and less conservative synchronization criteria are derived. Our results show that the outer synchronization can be achieved by impulsively controlling a crucial fraction of nodes in the response network. Finally, numerical examples are exploited to illustrate the effectiveness of our theoretical results.