Event-triggered delayed impulsive control for input-to-state stability of nonlinear impulsive systems

This paper studies the input-to-state stability (ISS) and integral input-to-state stability (iISS) of nonlinear impulsive systems in the framework of event-triggered impulsive control (ETIC), where the stabilizing effect of time delays in impulses is fully considered. Some sufficient conditions which can avoid Zeno behavior and guarantee the ISS/iISS property of impulsive systems are proposed, where external inputs are considered in both the continuous dynamics and impulsive dynamics. A novel event-triggered delayed impulsive control (ETDIC) strategy which establishes a relationship among event-triggered parameters, impulse strength and time delays in impulses is presented. It is shown that time delays in impulses can contribute to the stabilization of impulsive systems in ISS/iISS sense. Finally, the effectiveness of the proposed theoretical results is illustrated by two numerical examples.