广义马尔科夫跳变系统的滑模控制  

Sliding Mode Control for the Generalized Markovian Jump System

作　　者：杨冬梅[1] 杜玲秀 YANG Dongmei;DU Lingxiu(School of Sciences,Northeastern University,Shenyang 110819 China)

机构地区：[1]东北大学理学院,辽宁沈阳110819

出　　处：《西华大学学报（自然科学版）》2023年第4期82-87,95,共7页Journal of Xihua University:Natural Science Edition

基　　金：国家自然科学基金资助项目(61673100)。

摘　　要：研究广义马尔科夫跳变系统的H_(∞)容许性以及滑模控制器的设计。首先对系统设计了滑模面,然后引入李亚普诺夫泛函,得到了系统容许的线性矩阵不等式,通过自由权矩阵方法、加减项以及线性矩阵不等式方法,得到系统H_(∞)容许的充分条件;对滑模进行动力学分析,设计了一个滑模控制器,使得系统能在有限时间内到达滑模面上。最后,通过仿真结果验证了理论的有效性。The H_(∞) tolerance of the generalized Markov jump system and the design of the sliding mode controller are studied.Firstly,a sliding mode surface is designed for the system,and then Liapunov function is introduced to obtain the linear matrix inequality for the H_(∞) tolerance of the system,and the sufficient conditions for the tolerance of the system are obtained by the free power matrix method,the addition and subtraction terms,and the linear matrix inequality method.After that,the sliding mode dynamics is analyzed and a sliding mode controller is designed so that the system can be employed to reach the sliding mode surface in a finite time.Finally,the simulation results verify the effectiveness of the theory.

关 键 词：马尔科夫跳变系统 广义系统 滑模控制 滑模控制器 自由权矩阵 

分 类 号：O23[理学—运筹学与控制论] O316[理学—数学]