小参数时变非线性系统的技术稳定性

楚天广; 王照林

小参数时变非线性系统的技术稳定性

楚天广¹,
王照林²

1.
北京大学力学与工程科学系, 北京 100871;
2.
清华大学工程力学系, 北京 100084

基金项目: 国家自然科学基金资助项目(19872005);高等学校博士学科点专项科研基金资助项目(97000130);航天工业总公司五二研究所

详细信息

作者简介:
楚天广(1964- ),男,河南杞县人,副教授,博士;王照林(1928- ),男,山东掖县人,教授,博士生导师.

中图分类号: O175.21
计量
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- 被引次数: 0
出版历程
- 收稿日期: 1999-08-03
- 修回日期: 2000-05-25
- 刊出日期: 2000-11-15

Technical Stability of Nonlinear Time-Varying Systems With Small Parameters

CHU Tian-guang¹,
WANG Zhao-lin²

1.
Department of Mechanics and Engineering Science, Peking University, Beijing 100871, P R China;
2.
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P R China

摘要

摘要: 分析一类含小参数的时变非线性系统关于给定状态约束集合的技术稳定性.根据向量微分比较原理和基本的单调性准则,利用向量V函数方法给出由系统系数表达的技术稳定性判据.并讨论了基于派生系统和线性化方法研究非线性系统技术稳定性的条件.另外,对于派生时变线性系统的指数稳定性给出了简单的代数判据.最后给出示例说明文中方法.
- 时变非线性系统 /
- 小参数 /
- 技术稳定性 /
- 向量比较原理 /
- 派生系统 /
- 线性化方法 /
- 指数渐近稳定性
Abstract: Technical stability allowing quantitative estimation of trajectory behavior of a dynamical system over a given time interval was considered.Based on a differential comparison principle and a basic monotonicity condition,technical stability relative to certain prescribed state constraint sets of a class of nonlinear time-varying systems with small parameters was analyzed by means of vector Liapunov function method.Explicit criteria of technical stability are established in terms of coefficients of the system under consideration.Conditions under which the technical stability of the system can be derived from its reduced linear time-varying(LTV) system were further examined,as well as a condition for linearization approach to technical stability of general nonlinear systems.Also,a simple algebraic condition of exponential asymptotic stability of LTV systems is presented.Two illustrative examples are given to demonstrate the availability of the presently proposed method.
- nonlinear time-varying system /
- small parameter /
- technical stability /
- vector comparison principle /
- reduced system /
- linearization technique /
- exponential asymptotic stability

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参考文献(11)

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