Stabilization of Switched Systems With Unstable Subsystems via an Event-Triggered Control Based Codesign Method

Two state feedback based event-triggered stabilization methods for switched systems under both synchronous phenomenon and asynchronous phenomenon are proposed, where no subsystem of the resulting closed-loop switched systems is necessarily stable. The discontinuity of triggering conditions at switching instants of controllers or subsystems can result in the samplings instantaneously, which makes obtaining the positive minimum of inter-execution times to ensure Zeno-freeness phenomenon not applicable, thus two new methods are proposed to illustrate Zeno-freeness phenomenon of two event-triggering mechanisms. Moreover, using two methods can estimate the maximum sampling number in every interval with finite length. The event-triggered control based codesign method can guarantee exponential stability and asymptotic stability with Zeno-freeness behavior of systems under synchronous phenomenon and asynchronous phenomenon respectively. Moreover, sufficient conditions on the corresponding stability are developed. Finally, two examples are presented to illustrate the effectiveness of the proposed methods.