Event-triggered delayed impulsive control for functional differential systems on networks

This article investigates the stability of functional differential systems on networks adopting event-triggered multi-delayed impulsive control. We construct a new event-triggered mechanism (ETM) type using the Lyapunov function and the network topology. Combined with the ETM and multi-delayed impulsive control, in which the impulsive jumps are related to the current and past states, we propose a multi-delayed event-triggered impulsive control strategy. This controller will execute the control tasks only when the systems violate the preset ETM. In the view of the Razumikhin method and the graph theory, some criteria are given to avoiding Zeno behavior under this ETM and achieving exponential stability, which is related to the event-triggered parameters, network topology, and impulsive intensity. As an application of our theoretical results, a class of coupled oscillation systems is considered and numerical simulations are presented to verify the practicability and effectiveness.