【摘要】 针对一般随机线性时滞微分方程,给出了方程的平凡解的几乎必然指数稳定性的一个充分条件,由此利用时滞随机系统的比较原理建立一般时滞随机线性大系统的二阶矩指数稳定与几乎必然指数稳定新的代数判据.利用恰当的Lyapunov函数结合不等式技巧得到了这些条件.特别是用一个代数方程给出了依赖时滞的Lyapunov指数的估计.并用实例加以验证.更多还原

【Abstract】 For a class of general linear stochastic equation with time-delay,this paper presents a sufficient condition of guaranteeing the almost sure exponential stability of the trivial solution of the equation.From that,a new algebraic criterion of 2-order moment exponential stability and the almost sure exponential stability for general lineal stochastic large-scale system with time-delay is established by comparison theory.These conditions are derived by using suitable Lyapunov function method and combing with inequality technique.In particular,the Lyapunov exponent,which is depended on time-delay,is estimated by an algebraic equation.An example is given to verify the effectiveness of the results.更多还原