Period-sampled switching event-triggered control of discrete-time impulsive switched systems under two asynchronous behaviors

The event-triggered control (ETC) problem of discrete-time linear impulsive switched systems is addressed under two asynchronous behaviors. The coexistence of impulses, switching and triggering events causes two asynchronous phenomena: (1) the switching instants and impulsive instants may not necessarily be consistent with each other; (2) the mode of switching signals between the subsystem and the consequential controller is asynchronous. These two types of asynchrony not only induce instability seriously, but also pose great difficulties in avoiding the Zeno behavior of event-triggered mechanism (ETM). Regarding the above defects, a period-sampled switching event-triggered mechanism (PSSETM) is projected which covers the minimum dwell time, the relative threshold function and jump function to further reduce unnecessary resource waste and even effectively avoid Zeno behavior. Based on admissible edge-dependent average dwell time (AED-ADT) and admissible edge-dependent average impulsive interval (AED-AII) methods, constructive sufficient criteria for the global uniform exponential stability (GUES) of the closed-loop system are obtained. The improved solvability algorithm is also established through introducing a compensation term to event-triggered state feedback controller. Finally, an example is provided to demonstrate the effectiveness of the proposed strategy in our paper.