Synchronization of Switched Complex Dynamical Networks with Impulses: State-Dependent Switching Approach

This paper studies the globally exponential synchronization (GES) of a class of complex dynamical networks (CDNs) with switching topology involving impulse action. A novel state-dependent switching (SDS) approach to tune the switching topology of CDNs is designed based on the information of the node dynamics with impulses. Different from the traditional SDS results which are based on continuous state space, some sufficient conditions for network synchronization based on SDS are proposed in the framework of impulse action. A relationship between impulse action, the network structure, and switching topology is established, which is crucial to design the SDS law. Two different impulse actions on the network dynamics are fully considered in this paper, namely, stabilizing continuous dynamics with desynchronizing impulses and destabilizing continuous dynamics with synchronizing impulses. Finally, two numerical simulations are given to demonstrate the effectiveness of the proposed control method.