Stability analysis and design of switched normal systems

2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601) Pub Date : 2004-12-01 DOI:10.1109/CDC.2004.1428976

G. Zhai, Hai Lin, Xuping Xu, A. Michel

引用次数: 15

Abstract

In this paper, we study stability property for a class of switched systems whose subsystems are normal. The subsystems can be continuous-time or discrete-time. When all continuous-time subsystems are Hurwitz stable and all discrete-time subsystems are Schur stable, we show that a common quadratic Lyapunov function exists for the subsystems and that the switched system is exponentially stable under arbitrary switching. When unstable subsystems are involved, we show that given a desired decay rate of the system, if the activation time ratio between unstable subsystems and stable ones is less than a certain value (calculated using the decay rate), then the switched system is exponentially stable with the desired decay rate.

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切换正常系统的稳定性分析与设计

本文研究了一类具有正常子系统的切换系统的稳定性。子系统可以是连续时间的也可以是离散时间的。当所有连续时间子系统都是Hurwitz稳定，所有离散时间子系统都是Schur稳定时，我们证明了在任意切换情况下，系统是指数稳定的，并且存在一个共同的二次Lyapunov函数。当涉及不稳定子系统时，我们证明了给定系统的期望衰减率，如果不稳定子系统与稳定子系统之间的激活时间比小于某一值(使用衰减率计算)，则切换系统在期望衰减率下是指数稳定的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)

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