方程■+a■+f(■)+g(x)=0的全局渐进稳定性的一个新判据

A new criterion on the global asymptotic stability of the equation ■+a■+f(■)+g(x)=0

在运用李雅普洛夫第二方法研究非线性系统稳定性的时候,能否做出合适的李雅普洛夫函数是问题的关键.较好的李雅普洛夫函数带来较好的结果.由于做出了较好的李雅普洛夫函数,本文得以提供关于方程x…+ax··+f(x·)+g(x)=0的全局渐进稳定性的一个新判据.新判据推广了巴尔巴欣1952年和蒲利斯1955年的结果.

It is critical to construct a proper Liapunov function in the study of the stability of nonlinear system by Liapunov's second method. A better Liapunov function induces better results. Having constructed a better Liapunov function, this paper is able to offer a new criterion on the global asymptotic stability of the equation x …+a(x) ··+f((x))+g(x)=0, which extends both the result suggested by Barbashin in 1952 and the result suggested by Pliss in 1955.