择一定理在离散时间线性时不变系统中的应用  

Some Applications of Theorems of Alternatives in Discrete Time Linear Time-invariant Systems

作　　者：赵秋梅[1] 刘红英[1] 

机构地区：[1]数学,信息与行为教育部重点实验室北京航空航天大学数学系,北京100083

出　　处：《应用数学学报》2008年第2期352-358,共7页Acta Mathematicae Applicatae Sinica

基　　金：自然科学基金(10571010)资助项目．

摘　　要：基于广义择一定理,可以讨论离散时间线性时不变系统中的若干问题.首先可以利用广义择一定理得出Layaponov不等式的可行性与系统矩阵特征值的若干关系.其次利用这种广义择一定理讨论Ricaati不等式解的存在性,由此给出更一般KYP引理的简洁证明.In the light of the theorems of alternatives, some problems in discrete time linear time-invariant systems are discussed in this paper. Firstly, the connections of solvability of Lyapunov inequalities and eigenvalues of system matrix are discussed. Secondly, the exsistence of Riccati inequality is interpreted according to the theorems of alternatives. As a consequence, a simple proof of the general Kalman-Yakubovich-Popov（KYP） Lemma is given.

关 键 词：离散时间线性时不变系统 择一定理 线性矩阵不等式 KYP引理 

分 类 号：O224[理学—运筹学与控制论] O231[理学—数学]