基于LMI的离散广义系统正实控制器设计  

Design of Positive Real Controller for Discrete Descriptor Systems Based on LMIs

作　　者：靖新[1,2] 张庆灵[2] 郑莉[1] 杨晓光[2] 

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110004

出　　处：《沈阳建筑大学学报（自然科学版）》2008年第5期911-914,共4页Journal of Shenyang Jianzhu University：Natural Science

基　　金：辽宁省自然科学基金(20062003)

摘　　要：目的研究和解决离散型线性时不变广义系统的正实控制问题.方法通过分析离散型线性时不变广义系统正实性和无源性的关系,给出了在因果条件下新的正实引理.通过选择合适参数以及对受控系统进行化简和代数等价变换并基于线性矩阵不等式(LMI),给出了离散型线性时不变广义系统状态反馈正实控制器设计的充分条件.结果通过计算三个LMIs,给出了状态反馈正实控制器增益矩阵的求解方法,实现了离散型线性时不变广义系统的正实控制.结论针对带有外部干扰的离散型线性时不变广义系统,设计了正实状态反馈控制器,仿真算例表明,这种方法简单有效.For the discrete descriptor system, the positive real control problem is studied. By analyzing the relationships between the positive realness and passivity, a new lemma is derived in the condition of casual. By virtue of scalar method and some simple algebraic transformations, the state feedback controller is designed via the solvability of linear matrix inequality （LMI） with a new input. By solving LMIS, the sufficient con- ditions of positive realness state feedback control have loeen obtained. The obtained results can be applied to the strictly positive real feedback controller design. Furthermore, the positive realness and passivity of the closed loop system can be also guaranteed. Numerical simulation is carried out to show the consistency with the theoretical analysis in the paper.

关 键 词：离散 广义系统 正实 状态反馈 线性矩阵不等式. 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]