Event-Triggered Control of Switched Two-Time-Scale Systems With Asynchronous Switching

Abstract

This letter addresses the event-triggered control problem for uncertain switched two-time-scale systems (TTSSs) experiencing asynchronous switching. Due to ill-conditioning issues, methods developed for switched single-time-scale systems cannot be directly applied to switched TTSSs. Additionally, event-triggered results for non-switched TTSSs are inapplicable due to the complexities introduced by switching behavior and asynchronism. To address these challenges, we utilize a Lyapunov function dependent on the singular perturbation parameter and the controller mode to establish conditions sufficient to ensure the exponential stability of the closed-loop system with average dwell time switching. These conditions facilitate the joint design of a mode-dependent event-triggered mechanism and the control gains while mitigating the risk of Zeno behavior. Finally, a numerical example is provided to demonstrate the effectiveness and benefits of the proposed theorem.