非线性非自治系统零解的稳定性  

Stability of Zero Solution of Nonlinear and Nonautonomous System

作　　者：胡雅光[1] 蹇继贵[1] 

机构地区：[1]三峡大学理学院,湖北宜昌443002

出　　处：《三峡大学学报（自然科学版）》2008年第5期100-103,共4页Journal of China Three Gorges University：Natural Sciences

摘　　要：文章在允许Lyapunov函数的导数为变号函数的条件下,由微分方程的平凡解稳定,渐近稳定,一致渐近稳定的定义,通过直接证明,得到了非线性非自治微分方程的平凡解稳定,渐近稳定,一致渐近稳定的几个充分条件,这些定理改进了文献[1]的有关结论,对于检验非线性非自治微分方程的平凡解稳定,渐近稳定,一致渐近稳定具有重要意义.The problem of stability, asymptotic stability and uniform stability of trivial solution for nonlinear and nonautonomous systems is studied. A set of sufficient conditions of stability, asymptotic stability and uniform stability of trivial solution are given by utilizing I.yapunov function. These theorems allow the derivative of Lyapunov function to be not always of the same sign and improve the related theory in the literature [1]. Finally, two examples are given to illustrate the results.

关 键 词：非线性非自治系统 稳定性 渐近稳定性 一致稳定性 LYAPUNOV函数 

分 类 号：O231.2[理学—运筹学与控制论]