一类三阶非线性系统的全局渐近稳定性  

Globally Asymptotic Stability of a Class of Third Order Nonlinear System

作　　者：吴春雪[1] 时宝[1] 

机构地区：[1]海军航空工程学院数学研究所

出　　处：《烟台大学学报（自然科学与工程版）》2008年第2期83-85,共3页Journal of Yantai University(Natural Science and Engineering Edition)

基　　金：烟台大学青年基金资助项目(SX05Z9)

摘　　要：李雅普诺夫第二方法是研究非线性系统稳定性的基本方法之一,而Lyapunov函数的构造是解决问题的关键,本文运用"类比法"对非线性系统…x+g(x.)x¨+f(x.,x¨)x.+h(x)=0,构造了较好的Lyapunov函数,得到其平凡解全局渐近稳定的条件,并且证明中脱离了对Lyapunov函数无穷大性质的约束,推广了旧有的结果.The Lyapunov＇s second method is one of the basic methods to research the stability of nonlinear system. It is critical to construct a suitable Lyapunov function. In this paper, a better Lyapunov function of third order nonlinear system x ＋g（x）x ＋f（x,x）x ＋ h（x） =0 is constructed. The sufficient conditions for the globally asymptotically stability of trivial solution of the nonlinear systems is obtained, and the stronger condition of generally requiring Lyapunov function going to the infinite is removed, the results make further progress of some old results.

关 键 词：非线性系统 LYAPUNOV函数 全局渐近稳定性 

分 类 号：O175[理学—数学]