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. Note to Practitioners—As a scaled-down version of various industrial plant mechanisms, the industrial plant emulator setup consists of components such as servomechanisms, drives, conveyor belts, and assembly machines. This paper investigates the problem of impulsive control of industrial plant emulator setup. To achieve the Lyapunov stability of switched systems involving stable and unstable modes, the event-triggered impulsive control strategy which integrates the advantages of event-triggered control and impulsive control is proposed. Some sufficient conditions have been constructed in the framework of event-triggered impulsive control. Note that the information of the stable and unstable modes is considered and fully extracted into the design of control strategy. Hence, compared with the general event-triggered impulsive control strategies in which the continuous dynamics of stable modes are ignored, the control burden has been further alleviated. Moreover, the proposed theoretical results can be extended to practical applications, such as single-link robot arm systems, switched multi-agent systems, and automotive engine systems. In future, an interesting topic is to design event-triggered impulsive controller for stability of switched delay systems with dual modes.