Event-Triggered Impulsive Control for Switched Systems Involving Stable and Unstable Modes

This paper investigates the Lyapunov stability problem for switched systems involving stable and unstable modes under event-triggered impulsive control. By constructing multiple Lyapunov functions coupled with average dwell-time methods, some sufficient conditions on Lyapunov stability of switched systems involving stable and unstable modes are provided under event-triggered impulsive control. The designed event-triggered impulsive control strategy is mode-dependent, and Zeno behavior is eliminated. Then, with the construction of a connection between average dwell-time scheme and total dwell time of unstable modes, a relationship between mode-dependent event-triggered mechanism, system dynamics, and switching law is established. It plays a key role in designing event-triggered impulsive control with easy implementation. Moreover, this paper applies the theoretical results to the nonlinear switched system involving dual modes, in which an event-triggered impulsive control strategy is designed for the stability of the switched system. Finally, three numerical examples are given to verify the validity of the proposed results.