高维非线性随机微分方程组的指数稳定性

Exponential stability of high-dimensional nonlinearstochastic differential equations

随机系统的稳定分析,近年来逐渐受到很多概率论学者与工程技术人员的研究,并取得了重要的研究成果,而前人研究往往以Lyapunov方法为工具,从系统的生成元入手,得到系统稳定性的依据.文章从随机微分方程组的变换入手,将随机微分方程组局部的变换为带随机项的常微分方程组,然后通过类似于Hurwitz的分析技巧,从而得到系统的指数稳定性判据.

In recent years,the analysis of Stochastic system stability has been studied by a lot of probability theory research scholars and engineering technical personnel,and they have achieved important research results,the previous studies generally by means of Lyapunov method,from the generating element of the system which the stability of the system based on.In this paper,starting from the transformation of stochastic differential equations,stochastic differential equations are partially transformed into ordinary differential equations with random items.Afterwards,through analyzing skills similar to the Hurwitz,the exponential stability condition of the system is obtained.