Finite-time stability and stabilization of switched linear systems

Abstract

In this paper, finite-time stability and stabilization problems for switched linear systems are discussed. Firstly, the concept of finite-time stability is extended to switched linear systems. Then, based on the state transition matrix of the system, a necessary and sufficient condition for finite-time stability of switched linear systems is presented. For ease of reference, some sufficient conditions under which the switched linear systems are finite-time stable and uniformly finite-time stable are given by virtue of matrix inequalities. Moreover, stabilizing state feedback controllers and a class of switching signals with average dwell-time are designed in detail to solve finite-time stabilization problem. The main results are proved by using the multiple Lyapunov-like functions and common Lyapunov-like function respectively. Finally, two examples are employed to verify the efficiency of the proposed method.