随机线性系统依概率稳定的若干等价条件

Some equivalent conditions of stability in probability for stochastic linear systems

在系统分析与设计时 ,需要对系统的动态行为有所了解 .为此 ,讨论了It^o微分方程描述的线性随机系统依概率稳定性问题 .借助Cauchy矩阵 ,利用测度的单调性与连续性 ,得到了该类系统在概率意义下的稳定性 ,包括稳定、一致稳定、渐近稳定和全局稳定的若干充要条件 ,这些条件只与Cauchy矩阵的有界性和吸引性有关 .

The stability in probability for stochastic linear systems described by It differential equations were discussed. By using Cauchy matrix and monotony and continuity of measure, some equivalent conditions were obtained, which only depended on the boundedness and attractability of Cauchy matrix, to p stability of the systems, including stability, uniform stability, asymptotical stability and global stability.