Stability analysis for impulsive coupled systems on networks

This paper investigates the stability problem of equilibrium for impulsive coupled systems on networks (ICSNs). We provide a systematic method that allows one to construct global Lyapunov functions for large-scale impulsive coupled systems from building blocks of individual vertex systems by using results from graph theory. Consequently, a new asymptotic stability principle and a new exponentially stable principle, which have a close relation to the topology property of the network, are given. As an application to the results, we employ the principle to a class of impulsive coupled systems, and then an easy-verified sufficient condition which guarantees the asymptotic stability and exponential stability are obtained.