用扰动Lyapunov函数研究非线性微分方程关于初始时刻偏差的稳定性

数学物理学报 ›› 2011, Vol. 31 ›› Issue (2): 351-359.

用扰动Lyapunov函数研究非线性微分方程关于初始时刻偏差的稳定性

李安¹, 宋新宇², 王志祥³

1.厦门大学数学科学学院福建厦门 361005|2.信阳师范学院数学系河南信阳 464000; 3.解放军理工大学信息工程系南京 210007

收稿日期:2008-12-08 修回日期:2009-11-16 出版日期:2011-04-25 发布日期:2011-04-25
基金资助:
国家自然科学基金(10771179)、河南省高校科技创新团队支持计划(2010IRTSTHN006)和河南省科技创新杰出人才支持计划(104200510011)资助

Practical Stability of Nonlinear Differential Equations Relative to Initial Time Difference via Perturbing Lyapunov Functions

LI An¹, SONG Xin-Yu², WANG Zhi-Xiang³

1.School of Mathematical Sciences, Xiamen University, Fujian Xiamen 361005|2.Department of Mathematics, Xinyang Normal University, Henan Xinyang 464000|3.Department of Information and Electronic Engineering ICE, PLAUST, Nanjing 210007

Received:2008-12-08 Revised:2009-11-16 Online:2011-04-25 Published:2011-04-25
Supported by:
国家自然科学基金(10771179)、河南省高校科技创新团队支持计划(2010IRTSTHN006)和河南省科技创新杰出人才支持计划(104200510011)资助

摘要/Abstract

摘要：

该文研究了非线性微分方程关于初始时刻偏差的实用稳定性, 利用扰动Lyapunov函数得到了几个非线性动力系统关于初始时刻偏差的实用稳定性准则, 所得结论丰富了非线性微分方程关于初始时刻偏差的实用稳定性理论.

关键词: 实用稳定性, 比较原理, 初始时刻偏差, 扰动Lyapunov函数

Abstract:

In this paper, the practical stability of nonlinear differential equations with solutions starting off with different initial times is investigated. Several practical stability criteria of nonlinear dynamical systems relative to initial time difference are presented by perturbing Lyapunov functions. The results enrich the theory on practical stability of nonlinear differential equations relative to initial time difference.

Key words: Practical stability, Comparison principle, Initial time difference, Perturbing Lyapunov function

中图分类号:

34A37

李安, 宋新宇, 王志祥. 用扰动Lyapunov函数研究非线性微分方程关于初始时刻偏差的稳定性[J]. 数学物理学报, 2011, 31(2): 351-359.

LI An, SONG Xin-Yu, WANG Zhi-Xiang. Practical Stability of Nonlinear Differential Equations Relative to Initial Time Difference via Perturbing Lyapunov Functions[J]. Acta mathematica scientia,Series A, 2011, 31(2): 351-359.

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