Event-Triggered Impulsive Control for Input-to-State Stabilization of Nonlinear Time-Delay Systems

This article investigates the event-triggered impulsive control (ETIC) problem for a class of nonlinear time-delay systems subject to exogenous disturbances. An original event-triggered mechanism (ETM) which utilizes the information of system state and external input is constructed based on Lyapunov function approach. To achieve the input-to-state stability (ISS) of the considered system, some sufficient conditions are presented, in which the underlying relationship among ETM, exogenous input, and impulse action is established. Furthermore, the possible Zeno behavior induced by the proposed ETM is excluded simultaneously. As an application, the design criterion of ETM and impulse gain is put forward for a class of impulsive control systems with delay according to the feasibility of some linear matrix inequalities (LMIs). Finally, two examples with numerical simulations are provided to confirm the effectiveness of the developed theoretical results, where the synchronization issue of delayed Chua's circuit is considered.