Input-to-State Stability of Impulsive Systems via Event-Triggered Impulsive Control

This article investigates input-to-state stability (ISS) and integral ISS (iISS) of nonlinear impulsive systems based on the event-triggered impulsive control (ETIC) strategy, where the impulse sequence is generated by some predesigned event conditions. Unlike traditional event-triggered control, ETIC means that the controller is activated only when some state-dependent event conditions are triggered and moreover, there is not any control transmission between two consecutive triggered impulse instants. Event-triggered impulses are usually regarded as a class of state-dependent impulses, where the event-triggered mechanism (ETM) is an impulse generator. By using the ETIC strategy, some Lyapunov-based criteria are established, which can effectively avoid infinitely fast triggering behavior and guarantee ISS/iISS of nonlinear impulsive systems. Then, the theoretical results are applied to nonlinear system, where a class of ETMs and impulsive control gain are derived with the help of LMIs. Finally, two numerical examples are presented to illustrate the validity of our control strategies.