Exponential stabilization of asynchronously switched linear systems with constant time‐delay: Observer‐based event‐triggered control

Abstract

In this article, the exponential stabilization of an asynchronously switched linear system with constant time‐delay is studied by using continuous event‐triggered control. Aiming at reducing the communication and guaranteeing a satisfactory system performance, an observer‐based event‐triggered scheme is proposed with the introduction of an upper bound for the trigger interval. The cases of no trigger and multiple triggers within an interval of system switching are considered, respectively. Taking the system switching interval as a reference interval, the above two cases are modeled to establish a unified augmented closed‐loop system. A set of multiple Lyapunov‐Krasovskii functionals (LKFs) is constructed, the exponential stabilization of the switched system is studied based on the average dwell time (ADT) method and the constructed LKFs. Meanwhile, a LMI‐based design algorithm for the observer gain and the controller gain is given, respectively. In addition, the minimum lower bound of the trigger interval is determined to exclude the Zeno behavior. Two simulation examples are provided to demonstrate the effectiveness of the proposed results.