马尔可夫切换型随机微分方程解的几乎必然稳定性判据  

An criterion for almost sure exponential stability of stochastic differential equations with Markovian switching

作　　者：马洪强[1] 胡良剑[2] 王倩[3] 

机构地区：[1]复旦大学上海视觉艺术学院,上海201620 [2]东华大学应用数学系,上海200051 [3]西北民族大学计信学院,甘肃兰州730030

出　　处：《纺织高校基础科学学报》2009年第3期375-379,共5页Basic Sciences Journal of Textile Universities

摘　　要：近年来,马尔可夫切换型随机微分方程(MSDE)解的稳定性问题得到了广泛关注,但是用线性矩阵不等式(LMI)的方法来研究MSDE的几乎必然稳定性问题还未见报道.应用LMI来研究MSDE解的几乎必然稳定性问题,首先证明了MSDE解的几乎必然稳定性的一个Lyapunov定理,进而转化为LMI判据,最后通过一个数值例子说明了如何应用,其结果易于用Matlab工具箱进行检验.The stability of stochastic differential equations with Markovian switching （MSDE） have recently received much attention. However, almost surely exponential stability of MSDE has＇t been investigated by Linear Matrix Inequalities（LMI） method. Almost surely exponential stability of stochastic differential equations was discused with Markovian switching using linear matrix inequalities （LMIs）. First, a Lyapunov theorem has been proved and then converted it to LMI criterion which is easy to be checked in practice by using Matlab toolbox, to illustrate how to use the result of the paper, an example is given.

关 键 词：随机微分方程 几乎必然稳定 马尔可夫切换 布朗运动 线性矩阵不等式(LMI) 

分 类 号：O211.63[理学—概率论与数理统计]