Absolute exponential stability for a class of switched delay systems

Abstract

In this paper, we inspect the absolute stability of a class of special switched delay system. The linear part of the switched system is a fixed matrix, while the uncertain nonlinearity satisfies the sector contains. The absolute stability of the switched system in this paper is exponential stability under arbitrary switching. The concept of absolute exponential stability given in this paper extends many types of stability such as global asymptotical stability, global exponential stability, absolute stability and so on. Therefore, absolute exponential stability is a more meaningful concept. Firstly, we construct a class of Lyapunov functions, and give the sufficient conditions for the absolute stability of the system with linear matrix inequalities. Then, we consider the stabilization control of this system. Finally, we examine the feasibility of the proposed method by an example.