华东师范大学学报(自然科学版) ›› 2004, Vol. 2004 ›› Issue (4): 10-15.

• 数学 统计学 • 上一篇    下一篇

非线性离散动力系统稳定性的等价定理

汪志鸣1，郑毓蕃2，戴浩晖1   

  1. 1.华东师范大学数学系，上海200062; 2.华东师范大学计算机系，上海200062
  • 收稿日期:2003-03-14 修回日期:2003-04-19 出版日期:2004-12-25 发布日期:2004-12-25
  • 通讯作者: 汪志鸣

Equivalent Theorems for Various Uniform Stabilities of Discrete-time Nonlinear Systems

WANG Zhi-ming1，ZHENG Yu-fan2，DAI Hao-hui1   

  1. 1. Department of Mathematics，East China Normal University，Shanghai, 200062,China;2. Computer Sciences Department，East China Normal University，Shanghai, 200062,China
  • Received:2003-03-14 Revised:2003-04-19 Online:2004-12-25 Published:2004-12-25
  • Contact: WANG Zhi-ming

摘要： 证明了用K类函数表示的离散动力系统一致稳定和一致渐近稳定的等价定理，进而给出用KL函数刻划的一致渐近稳定判定定理及其逆定理.从而对于离散时间动力系统的扰动分析和相应控制问题研究莫定了严格的理论基础.

关键词: 非线性系统, 自动控制, 离散动力系统, 非线性系统, 自动控制, 离散动力系统

Abstract: Equivalent theorems in terms of class K functions are presented for uniform stability and uniform asymptotic stability of discrete-time nonlinear systems. On the base of the equivalent theorems, the theorem of uniform asymptotic stability for the discrete-time nonlinear systems and its comverse theorem are also obtained.

Key words: automatic control, discrete-time dynamics, nonlinear svstems, automatic control, discrete-time dynamics

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