具有时间滞后的随机大系统稳定性

摘要

为了确定随机因素对车辆系统等关联大系统的影响,基于向量Lyapunov函数法,研究一类具有变时滞的随机线性关联系统的稳定性.根据有关的随机微分不等式的稳定性,导出了系统指数稳定的充分条件.运用系统的系数矩阵和相应的Lyapunov矩阵方程的解构造判定条件,来判定时滞随机大系统的稳定性.最后给出一个仿真实例,验证了所得结论.%In order to make sure the effects of random factor for the vehicle systems, the stability for a class of stochastic interconnected systems with time varying delay was analyzed by constructing a vector Lyapunov function. A Sufficient condition was concluded for exponential stability of the systems. It is obtained that a stochastic is described as exponential stable if the conditon is satisfied, where the condition is constructed by employing the coefficient matrices of the system and the solutions of the Lyapunov equations which are interconnected with the system. Finally, a simulation example is given to illustrate how to apply the obtained results.