一类非线性pantograph混合随机微分方程的定性分析

Qualitative Analysis of a Kind of Nonlinear Pantograph Hybrid Stochastic Differential Equation

研究了下列非线性pantograph混合随机微分方程dx(t)=f(x(t),x(θ1t),t,r(t))dt+g(x(t),x(θ2t),t,r(t))dB(t),t≥0的零解的指数稳定性.利用随机微分方程的相关理论与M-矩阵理论,得到方程的零解的渐近有界性、p-阶指数稳定、几乎必然指数稳定和H∞稳定.推广了已有文献中的相关结论.

The exponential stability of the trivial solution of the following nonlinear pantograph hybrid stochastic differential equation dx(t)=f(x(t),x(θ1t),t,r(t))dt+g(x(t),x(θ2t),t,r(t))dB(t),t≥0 is discussed.By using the corresponding theory of stochastic differential equations and M- matrices theory,asymptotic boundedness,pth moment exponential stability and H∞ stability of the trival solution of the above equation are obtained.These criteria have generalized the corresponding results in some existing papers.