Prescribed-Time Control of Switched Systems: An Event-Triggered Impulsive Control Approach

This article focuses on prescribed-time control for nonlinear switched systems using event-triggered impulsive control. Taking into account different characteristic among each mode, two types of mode-dependent event-triggered mechanisms are presented with mode-dependent Lyapunov functions and tunable exponential parameters, which substantially reduce the update times of controller. It shows that, the interevent times, under the designed mode-dependent event-triggered mechanism, have a uniform lower bound and then do not exhibit Zeno behavior. Further, using Lyapunov approach, some sufficient conditions for prescribed-time stability are obtained, where a relationship among triggering parameter, impulse strength, and prescribed time is established explicitly. As an application, the proposed methods are proved to be applicable to switched control systems, where a class of LMI-based hybrid control approaches, including switching control and event-triggered impulsive control, is developed. The effectiveness of our presented event-triggered impulsive control is illustrated through two examples.