离散广义系统的严格耗散分析与控制  

Strictly dissipative analysis and control for discrete-time descriptor systems

作　　者：李琴[1] 靖新[1] 张庆灵[1] 衣娜[1] 

机构地区：[1]东北大学系统科学研究所,辽宁沈阳110004

出　　处：《控制理论与应用》2008年第3期462-467,474,共7页Control Theory & Applications

基　　金：国家自然科学基金(60574011);辽宁省普通高校学科带头人基金(124210)．

摘　　要：对离散广义系统,考虑了关于二次型供给率严格耗散控制问题.建立了严格耗散与扩展严格正实之间的等价性.利用线性矩阵不等式(LMI),给出了离散广义系统严格耗散的充分必要条件,并着重推导了其成立的严格LMI条件.针对输入向量维数等于状态向量维数的系统.分别利用非严格LMI及严格LMI,讨论了状态反馈下的严格耗散控制问题,并给出控制器的设计方法.也讨论了输入向量维数小于状态向量维数的情况.最后通过仿真算例说明所给方法的有效性和普遍性,同时显示了严格LMI条件在耗散控制问题中,比非严格LMI具有的优势.For discrete-time descriptor systems, we consider the problem of strictly dissipative control with quadratic supply rate. Equivalence between the strict dissipativity and the extended strictly positive realness is established. By using the linear matrix inequality （LMI）, we derive the necessary and sufficient conditions for discrete-time descriptor systems to be strictly dissipative, and provide the conditions in the form of strict LMI. When the dimension of input equals the dimension of state, we discuss the state-feedback dissipative control by means of the non-strict LMI and the strict LMI, respectively, and present the design method for the controller. We also discuss the case where the dimension of input is lower than the dimension of state. Numerical examples illustrate the effectiveness and universality of the proposed method, and show the advantages of the strict LMI condition over the non-strict LMI condition in the dissipative problem.

关 键 词：离散广义系统 耗散控制 线性矩阵不等式 状态反馈 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]