Exponential Stability and Asynchronous Stabilization of Impulsive Switched Systems with Admissible Edge-dependent Average Dwell Time

This paper studies the exponential stability and asynchronous stabilization problems for continuous-time impulsive switched systems with the method of admissible edge-dependent average dwell time. Here, the asynchronous behavior implies that the switches between the subsystems and controllers are asynchronous. Firstly, the sufficient conditions for the closed-loop impulsive switched system to be exponentially stable are investigated. Then, on the basis of the stability results, a new type of state-feedback controllers are designed. Furthermore, the asynchronous behavior is considered for the closed-loop system and a novel set of admissible edge-dependent controllers are designed. It is shown that the exponential stability and asynchronous stabilization of the closed-loop impulsive switched system can be achieved under the proposed control protocols. And the results are formulated in the form of feasible LMIs and the superiority of admissible edge-dependent average dwell time over traditional dwell time approach is further analyzed. Moreover, the results can be extended to study the asynchronous stabilization of switched systems. Finally, some illustrative examples are given to demonstrate the effectiveness of the results.