一类三阶非线性系统的全局渐近稳定性

Global Asymptotical Stability of a Class of Three-Order Nonlinear System

Lyapunov第二方法在非线性系统的稳定性研究中是十分有效的,然而在非线性系统中Lyapunov函数的构造却没有什么通用的方法.本文运用类比法构造Lyapunov函数,讨论了三阶非线性系统…x+g(x¨)+f(x,x.)x.+cx=0和…x+g(x.)x¨+f(x,x.)x.+cx=0的稳定性,并给出其零解全局渐近稳定的充分性准则,文末一个简洁的例子说明本文主要结果的有效性.

Liapunov＇s second method is a very effective one in the study of the stability of nonlinear systems. However, there aren＇t universal methods in constructing the Lyapunov function of nonlinear system. In this paper, the Lyapunov function by use of comparison method is constructed, and the stability of a class of three-order nonlinear system x ＋ g（x） ＋f（x,x）x ＋ cx = 0 and x ＋ g（x） x ＋f（x ,x） x ＋ cx = 0 is discussed, some sufficient conditions of global asymptotical stability of its zero solution have been obtained. In the end of the paper, a concise example is given to illustrate the validity of the main result of this paper.