奇异Ito随机系统几个重要基础问题的研究进展  

Research advances of several important and basic problems for singular It stochastic systems

作　　者：赵勇[1] 张维海[2] 

机构地区：[1]山东科技大学数学与系统科学学院,青岛266590 [2]山东科技大学电气与自动化工程学院,青岛266590

出　　处：《南京信息工程大学学报（自然科学版）》2017年第3期237-245,共9页Journal of Nanjing University of Information Science & Technology（Natural Science Edition）

基　　金：国家自然科学基金(61573227)

摘　　要：近年来,一类由It随机微分方程驱动的奇异随机系统因其在实际领域中的广泛应用而备受关注.然而,系统方程同时包含奇异矩阵和扩散矩阵,大大增加了分析问题的复杂性.本文首先概述了奇异It随机系统几个重要基础问题的研究进展,主要包括:系统方程解的存在条件、广义It公式、容许性定义及稳定性问题.同时针对不同文献对上述问题的研究结果提出了自己的观点.最后对以上基础问题研究待解决的问题进行了展望.In recent years, singular stochastic systems governed by the Ito^ stochastic differential equation have received much attention due to their extensive applications to some practical areas.However, it is very complicated to discuss singular stochastic systems since the system equation includes both the singular matrix and the diffusion matrix simultaneously.In this paper, research development of several important and basic problems for singular Ito^ stochastic systems are concluded, including mainly the existence condition for the solution to the system equation, the general Ito^ formula, the definition of admissibility and the issue of stability.Also, some research perspectives are given for results of different references.Finally, some prospects to the unresolved problems are presented.

关 键 词：奇异Ito随机系统 解的存在条件 广义Ito公式 容许性 稳定性 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]