Event-triggered distributed delayed impulsive control for nonlinear systems with applications to complex networks

This paper studies the Lyapunov stability of general nonlinear systems and the synchronization of complex networks via event-triggered impulsive control (ETIC), where the distributed delayed impulses are fully considered. Some sufficient conditions are given to deal with the problem of Lyapunov stability for nonlinear systems and avoid Zeno behavior based on distributed delayed ETIC. Moreover, some relationships between the distributed delays in impulses, the triggering parameters, and the impulsive parameters are constructed. Then, as an application, we apply the above theoretical results to complex networks and design a kind of distributed delayed ETIC strategy to ensure synchronization of complex networks under distributed delayed ETIC. In the end, the validity of our proposed results is proved by two numerical examples.