The problem of exponential stability for a class of switched nonlinear systems with discrete and distributed time-varying delays is studied. The constraint on the derivative of the time-varying delay is not required which allows the time delay to be a fast time-varying function. We study the stability properties of switched nonlinear systems consisting of both stable and unstable subsystems. Average dwell-time approached and improved piecewise Lyapunov functional combined with Leibniz-Newton are formulated. New delay-dependent sufficient conditions for the exponential stabilization of the switched systems are first established in terms of LMIs. A numerical example is also given to illustrate the effectiveness of the proposed method. 1. Introduction The switched systems are an important class of hybrid systems. They are described by a family of continuous or discrete-time subsystems and a rule that orchestrates the switching between the subsystems. Recently, switched systems have attracted much attention due to the widespread application in control, chemical engineering processing , communication networks, traffic control [2, 3], and control of manufacturing systems [4–6]. A switched nonlinear system with time delay is called switched nonlinear delay system, where delay may be contained in the system state, control input, or switching signals. In [7–9], some stability properties of switched linear delay systems composed of both stable and unstable subsystems have been studied by using an average dwell-time approach and piecewise Lyapunov functions. It is shown that when the average dwell time is sufficiently large and the total activation time of the unstable subsystems is relatively small compared with that of the Hurwitz stable subsystems, global exponential stability is guaranteed. The concept of dwell time was extended to average dwell time by Hespanha and Morse  with switching among stable subsystems. Furthermore,  generalized the results to the case where stable and unstable subsystems coexist. The stability analysis of nonlinear time-delay systems has received increasing attention. Time-delay systems are frequently encountered in various areas such as chemical engineering systems, biological modeling, and economics. The stability analysis for nonlinear time-delay systems has been investigated extensively. Various approaches to such problems have been proposed, see [12–14] and the references therein. It is well known that the existences of time delay in a system may cause instability and oscillations system. Thus, the stability analysis
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