一类伊藤型广义随机系统的有限时间稳定性  

Finite-Time Stability of Singular Stochastic Systems with the It Type

作　　者：邢双云[1,2] 张庆灵[2] 赵德平[1] 

机构地区：[1]沈阳建筑大学理学院,辽宁沈阳110168 [2]东北大学系统科学研究所,辽宁沈阳110819

出　　处：《沈阳建筑大学学报（自然科学版）》2014年第3期572-576,共5页Journal of Shenyang Jianzhu University：Natural Science

基　　金：国家自然科学基金项目(61273008)

摘　　要：目的研究一类具有伊藤(It)型的广义随机系统分析与控制问题.方法广义系统有限时间稳定性概念,引入一个新的广义随机系统有限时间稳定性概念,它被定义为有限时间随机稳定性.利用伊藤微积分理论、随机控制理论、线性矩阵不等式等理论研究分析与控制问题.结果给出了伊藤型广义随机系统有限时间随机稳定的充分条件;并且在具有固定参数的严格线性矩阵不等式上,设计状态反馈控制器算法保证所得的闭环广义随机系统是有限时间随机稳定,同时给出相应的有限时间随机稳定的充分条件.结论所提出的方法能很好地解决随机干扰情况下,广义系统的有限时间稳定性问题,通过两个数值算例可以说明所提方法的有效性和可行性.The analysis and control problem of the finite-time stability for singular stochastic systems with the type are investigated. Combined with the finite time stability concept of singular systems, a new finite-time stability concept for singular stochastic systems which is defined as finite-time stochastic stability is introduced. Using Ito^ calculus theory, the stochastic control theory and linear matrix inequality （LMI） theory, the analysis and control problem of the finite-time stability for singular stochastic systems are investigated. A sufficient condition of finite-time stochastic stability is obtained for singular stochastic systems. In the sequence, designed algorithm for state feedback controller is provided to ensure that the underlying closed-loop singular stochastic system is finite-time stochastic stability in terms of strict linear matrix equali- ties with a fixed parameter, and the corresponding sufficient condition of finite-time stochastic stability is given as well. The proposed method can be better solved the finite-time stability problem for singular systems with random disturbance, two illustrative examples are presented to show the validity and novelty of the obtained results.

关 键 词：广义随机系统 伊藤微分 有限时间随机稳定 线性矩阵不等式 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]