作　　者： ; ;

机构地区： 佛山科学技术学院理学院信息科学与数学系

出　　处： 《佛山科学技术学院学报（自然科学版）》 2003年第2期1-5,共5页

摘　　要： 建立了具有非线性反馈的随机时变滞后系统的比较原理 ,并用比较原理给出了系统依概率稳定、依概率渐近稳定、 p阶均值稳定、 p阶均值渐近稳定的判别准则。 This paper considers the system of stochastic differential equations with nonlinear feedback through randomly time varying delays x·(t,ω)=A(t,ω)x(t,ω)+B(t,ω)f(z(t-y(t,ω),ω)), where z(t,ω)=C(t,ω)x(t,ω).The n 2 elements of A,n 2 elements of B,n 2  elements of C, and the delays are combined into a vector ξ. It is assumed the process {ξ(t,ω):t≥t 0} is an almost surely bounded right continuous strong Markov process, and f(x) is a nonlinear function which satisfies a Lipschitz continuity condition. By employing vector Lyapunov like functions and the theory of systems of delay differential inequalities, a very general comparison theorem for the above systems is developed. Furthermore, sufficient conditions are given for the stability of solutions in probability and in the p order mean.

关 键 词： 随机时滞系统 依概率稳定 阶均值稳定 比较原理

领　　域： [理学] [理学]