Markovian跳变不确定分布参数系统随机稳定性分析  

Stochastic Stability of Markovian Jump Uncertain Distributed Parameter Systems

作　　者：李延波 陈超洋[2] 欧阳 卜子云 LI Yan-bo;CHEN Chao-yang;OU Yang;BU Zi-yun(School of Information and Statistics,Guangxi University of Finance and Economics,Nanning 530001,China;School of Information and Electrical Engineering,Hunan University of Science and Technology,Xiangtan 411201,China;School of Logistics Management and Engineering,Nanning Normal University,Nanning 530001,China)

机构地区：[1]广西财经学院信息与统计学院,广西南宁530001 [2]湖南科技大学信息与电气工程学院,湖南湘潭411201 [3]南宁师范大学物流管理与工程学院,广西南宁530001

出　　处：《控制工程》2022年第1期109-113,共5页Control Engineering of China

基　　金：国家重点研发计划“政府间跨国合作”项目重点专项(2019YFE0118700);国家自然科学基金资助项目(61973110,71961002);广西财经学院博士科研启动项目(BS2019002);湖南省湖湘青年英才科技创新人才项目(2020RC3048);湖南省自然科学杰出青年基金资助项目(2021JJ10030)。

摘　　要：研究了一类具有Markovian跳变的不确定分布参数系统的随机稳定性问题。基于线性矩阵不等式方法,通过构造适当的随机Lyapunov泛函,计算弱无穷小算子,利用Green公式及Schur补引理,系统随机稳定的充分条件以一组线性矩阵不等式给出。线性矩阵不等式很容易通过MATLAB中的LMI工具箱进行求解。该充分条件便于工程实际应用。最后,构建仿真模型验证了该方法的有效性。Stochastic stability of a class of Markovian jump uncertain distributed parameter systems is researched in this paper.Based on linear matrix inequality approach,the sufficient conditions for the stochastic stability of the systems are given in terms of a group of linear matrix inequalities by constructing the appropriate Lyapunov functions,calculating weak infinitesimal generator,taking advantage of Green formula and Schur complement lemma.The linear matrix inequalities can be solved easily by LMI toolbox in MATLAB.The sufficient conditions are applied to engineering practice conveniently.At last,a simulation model is built to verify the effectiveness of the method.

关 键 词：Markovian跳变 分布参数系统 随机稳定性 不确定性 线性矩阵不等式 

分 类 号：O175[理学—数学]