Synchronization Control of Complex Dynamical Networks: Invariant Pinning Impulsive Controller with Asynchronous Actuation

This article revisits the pinning impulsive control issue for complex dynamical networks (CDNs) using a new invariant pinning impulsive strategy. The word invariant means that the set of pinned nodes is fixed and does not change throughout the control process. First, it is revealed that each pinning strategy can naturally induce a hierarchical network structure. Based on that, a new multi-layer method is proposed to realize the invariant pinning. Next, under some mild assumptions, distinct Zeno-free controllers are designed using the event-triggered fashion in each layer of the network. Different from most existing works, the design of events here allows asynchronous actuation of the impulsive controllers. Then, the proposed strategy is proved to be also effective for impulsive sequences subject to average impulsive interval (AII). Finally, numerical examples are provided to show the validity of the main results, even for large scale networks or chaotic systems.