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.
出处
《应用数学学报》
CSCD
北大核心
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．
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
discrete time linear time-invariant systems
theorems of alternatives
linear matrix inequality（LMI）
Kalman-Yakubovich-popov（KYP） lemma
