| 非线性时变离散系统的稳定性判据 |
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| 引用本文： | 于素娟,汪志鸣.非线性时变离散系统的稳定性判据[J].华东师范大学学报(自然科学版),2007,2007(1):47-50. |
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| 作者姓名： | 于素娟 汪志鸣 |
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| 作者单位： | 华东师范大学,数学系,上海,200062 |
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| 基金项目： | 国家自然科学基金
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上海市重点学科建设项目 |
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| 摘 要： | 用Lyapunov方法研究非线性时变离散系统的渐近稳定性. 如果存在与时间无关的正定Lyapunov函数, 它沿着系统的轨道不增, 同时附加类似于Barbashin-Krasovskii定理中描述的一个条件时, 即可得到渐近稳定的结论. 将此结果分别应用到自治系统和周期系统时,即可得离散情况下的LaSalle定理和Barbashin-Krasovskii定理.
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| 关 键 词： | 一致渐近稳定 时变系统 Lyapunov方法 一致渐近稳定 时变系统 Lyapunov方法 |
| 文章编号： | 1000-5641（2007）01-0047-04 |
| 收稿时间： | 2005-12 |
| 修稿时间： | 2005-12 |
Stability Criterion for Nonlinear Time-Varying Discrete-time Systems(Chinese) |
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| YU Su-juan,WANG Zhi-ming.Stability Criterion for Nonlinear Time-Varying Discrete-time Systems(Chinese)[J].Journal of East China Normal University(Natural Science),2007,2007(1):47-50. |
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| Authors: | YU Su-juan WANG Zhi-ming |
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| Institution: | Department of Mathematics, East China Normal University, Shanghai 200062, China |
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| Abstract: | The asymptotic stability of nonlinear time-varying discrete-time systems was studied by using Lyapunov approach.If there exists time independent Lyapunov function V that is positively definite,and its difference is non-increased along the solutions of the systems,plus the additional condition imposed as the one of statements of the Barbashin-Krasovskii theorem,the conclusion of asymptotic stability will be obtained. In applications of Theorem 1 to the time-invariant and periodic systems respectively,the LaSalle theorem and Barbashin-Krasovskii theorem can be reobtained. |
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| Keywords: | asymptotic stability time-varying systems Lyapunov approach |
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