Input-to-State Stability of Nonlinear Time-Delay Coupled Systems on Networks With Delay-Dependent Impulses

In this paper, the input-to-state stability (ISS) problem is addressed for nonlinear delayed coupled systems on networks (CSNs) with delay-dependent impulses. Utilizing graph theory and Lyapunov-Krasovskii method, an ISS Lyapunov function for the entire network is formulated built upon the ISS Lyapunov functions of individual vertex systems and sufficient conditions of ISS for general nonlinear delayed impulsive coupled systems on networks are obtained. It is shown that, when every continuous vertex system is ISS, the nonlinear delayed impulsive coupled systems according to a directed graph can still maintain ISS property provided destabilizing impulses occur infrequently. Compared with the existing results on impulsive CSNs, our results are more general and easier to verify. Additionally, we provide a simulation example to demonstrate the usefulness of the obtained results.