高维非线性系统的稳定性

The Stability Of Nonlinear System Of High Degree

本文运用连续定号但不一定可导的函数 V(x)来判定非自治非线性系统零解的稳定性,得到了如果 V(x(t))关于 t 单调增加(减少),其中 x(t)为给定系统的解,则所给系统的零解稳定.并且给出了判断 V(x(t))单调的准则.运用所得结果于自治系统可来判定其零解的渐近稳定性.

In present paper,we apply the conflnuous function V(x) with definite sign,but not always differentiableto discuss the stability of the zero solution of given non-autonomous system.We obtain that the zero so-lution of given equation is stable,if V(x(t) is monotonic about t,where x(t) is the solution of thesame sytem.For some V(x),we give the sufficient conditions that the V(x(t))is monotonic about t,from which the problem of stability can be solved.