马尔可夫跳变系统的有限时间保性能控制  

Finite-time guaranteed cost control for Markov jump systems

作　　者：王俊 姚凤麒 程培[2] WANG Jun;YAO Fengqi;CHENG Pei(School of Electrical and Information Engineering,Anhui University of Technology,Maanshan 243032,China;School of Mathematical Sciences,Anhui University,Hefei 230601,China)

机构地区：[1]安徽工业大学电气与信息工程学院,马鞍山243032 [2]安徽大学数学科学学院,合肥230601

出　　处：《南京信息工程大学学报》2024年第2期186-192,共7页Journal of Nanjing University of Information Science & Technology（Natural Science Edition）

基　　金：国家自然科学基金(11771001);安徽省高校自然科学基金(2022AH050108)。

摘　　要：本文主要研究具有时变时滞的脉冲随机马尔可夫跳变系统的有限时间保性能控制问题.通过选取模态相关的李雅普诺夫泛函,使用线性矩阵不等式(LMI)、平均驻留时间方法等技术,得到一些新的充分条件来确保系统有限时间稳定,并给出了系统的上界性能指标.基于该充分条件设计了系统的状态反馈保性能控制器.最后,利用Matlab的LMI工具箱进行数据仿真,得到相应的均方轨迹图.数值例子结果表明,得到的仿真结果和理论结果一致,验证了文中理论的有效性.The finite-time guaranteed cost control problem is studied for impulsive stochastic Markov jump systems with time-varying delays.By selecting mode-dependent Lyapunov functionals,using techniques such as Linear Matrix Inequality(LMI)and average dwell time,we obtain some new sufficient conditions to ensure finite-time stability and the upper bound performance index of the system,hence design a guaranteed cost controller with state feedback.Finally,the LMI toolbox of Matlab is used for data simulation,and the corresponding mean-square trajectory plots are obtained.Numerical examples show that the obtained simulation results are consistent with the theoretical results,which verifies the effectiveness of the proposed approach.

关 键 词：有限时间稳定 马尔可夫跳变 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]