Abstract
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.
Highlights
We study the stability properties of switched nonlinear systems consisting of both stable and unstable subsystems
The switched systems are an important class of hybrid systems
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
Summary
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. 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. Hien and Phat 23 presented exponential stability and stabilization conditions for a class of uncertain linear system with time-varying delay, based on an improved Lyapunov-Krasovskii functional combined with Leibniz-Newton formula. The problem of exponential stability for a class of switched nonlinear systems with discrete and distributed time-varying delays is studied. Average dwell-time approached and improved piecewise Lyapunov functional combined with Leibniz-Newton’s formula, and new delay-dependent sufficient conditions for the exponential stabilization of the switched systems are first established in terms of LMIs. A numerical example is given to illustrate the effectiveness of the proposed method.
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