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·
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.
出处
《应用数学和力学》
EI
CSCD
北大核心
2000年第11期1140-1146,共7页
Applied Mathematics and Mechanics
基金
国家自然科学基金资助项目!( 19872 0 0 5)
高等学校博士学科点专项科研基金资助项目!( 970 0 0 130 )
航天工业总公司五 二研究所
关键词
时变非线性系统
小参数
技术稳定性
向量比较原理
指数渐近稳定性
nonlinear time_varying system
small parameter
technical stability
vector comparison principle
reduced system
linearization technique
exponential asymptotic stability
