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研究分布式迭代随机大系统的均方渐近收敛性，得到一些收敛性判据．文中处理的子系统是具有多个噪声的随机系统．关于孤立随机子系统的基本假设就是其均方收敛的充要条件，在大系统的关联项中也假设存在随机噪声．文中对随机子系统的均方渐近收敛性作了详细的研究，给出了判断其均方渐近收敛性的两种途径：Ｒｏｕｔｈ＿Ｈｕｒｗｉｔｚ判据和数值计算方法．文中尤其研究了一类优化问题，以减小所得分布式迭代随机大系统的均方渐近收敛性判据的保守性．
The mean square asymptotic convergence of distributed iterative stochastic systems is studied, and some convergence criteria are obtained. The subsystem dealt with in this paper is a random system with multiple noises. The basic assumption about the isolated stochastic subsystems is the necessary and sufficient condition for its mean-square convergence. Suppose there is random noise also in the related items of the large system. In this paper, the mean square asymptotic convergence of the stochastic subsystems is studied in detail. Two approaches to determine the asymptotic convergence of the mean square are given: the Routh_Hurwitz criterion and the numerical method. In particular, a class of optimization problems are studied in this paper to reduce the conservation of mean square asymptotic convergence of the resulting distributed iterative stochastic large-scale systems.