华东师范大学学报(自然科学版) ›› 2007, Vol. 2007 ›› Issue (1): 47-50.

• 数学 • 上一篇    下一篇

非线性时变离散系统的稳定性判据

于素娟, 汪志鸣   

  1. 华东师范大学 数学系, 上海 200062
  • 收稿日期:2005-12-01 修回日期:2006-05-26 出版日期:2007-01-25 发布日期:2007-01-25
  • 通讯作者: 汪志鸣

Stability Criterion for Nonlinear Time-Varying Discrete-time Systems(Chinese)

YU Su-juan, WANG Zhi-ming   

  1. Department of Mathematics, East China Normal University, Shanghai 200062, China
  • Received:2005-12-01 Revised:2006-05-26 Online:2007-01-25 Published:2007-01-25
  • Contact: WANG Zhi-ming

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.

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

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.

Key words: time-varying systems, Lyapunov approach, asymptotic stability, time-varying systems, Lyapunov approach

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