利用V函数研究非线性系统解的稳定性

The Stability of Some Nonlinear Differential Equations by Using Liapunov Function

该文用李雅普诺夫(Liapunov)的第二方法分析了一类三阶非线性微分系统x+φ(x)f(x)+g(x)+h(x)=0(1)零解的稳定性。在常系数线性系统的李雅普诺夫函数的基础上,通过变换找到该系统的等价线性系统,采用线性类比的方法构造出合适的李雅普诺夫函数,从而得出了这个系统的零解是渐近稳定的一组充分条件。

In this paper, we analyze the stability of a class of nonlinear differential equations like x^···＋φ（x）f（x^··）＋g（x^·）＋h（x）=0（1） by using the second method of Liapunov. Based on Liapunov function, which is constant coefficient of linear Systems, first we transform this system into its corresponding equivalent linear systems. Then by using ＂linear comparison method＂, we construct a suitable Liapunov Function to investigate this system. In the end, we obtain a set of sufficient conditions of the stability of the zero solution asymptotically for this system.