大型分布式迭代随机系统的均方渐近收敛性

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．

MEAN_SQUARE ASYMPTOTIC CONVERGENCE OF LARGE SCALE DISTRIBUTED ITERATIVE STOCHASTIC SYSTEMS *

In this paper the mean_square convergence of large_scale distributed iterative stochastic systems is investigated, and some mean_square convergence criteria are obtained. The sub_systems dealt with are stochastic systems with multi_noises. The basic assumptions on the isolated sub_systems are just the necessary and sufficient conditions for the mean_square convergence. It is also assumed that there are stochastic noises in the interconnection terms of the large_scale systems. A detailed investigation on the mean_square convergence of the sub_systems is also carried out. Two approaches of determining the mean_square convergence of the sub_systems by the Routh_Hurwitz criterion and by numerical computation are given, together with an optimization problem, which leads to less conservation of the mean_square convergence criteria obtained for the large_scale stochastic systems.