Exponential stability analysis and stabilization of switched delay systems

Abstract

This paper investigates the problems of exponential stability analysis and stabilization for switched systems with time-varying delay via a new approach. To study the problems, the original system is transformed into an interconnection system, which is composed of a feedback subsystem and a forward one with a constant delay and an uncertainty disturbance. The exponential stability condition is presented to guarantee the α-input–output stability of the interconnection system based on the scaled small gain theorem, which is further proved to guarantee the exponential stability of the original system under arbitrary switching signal. Then the switching law existence condition is also proposed for exponential stabilization without input signal. Moreover, the problem of stabilization is further solved with admissible controllers obtained via convex optimizations. Both the problems are solved based on the model transformation method and the input–output approach. The merit of the proposed results lies in its reduced conservatism, which is made possible by a precise approximation of the time-varying delay and the scaled small gain theorem. The superiority and effectiveness of our results over the existing ones are illustrated via some numerical examples.