The Kalman-Yakubovich-Popov lemma in a behavioural framework and polynomial spectral factorization
The Kalman-Yakubovich-Popov lemma in a behavioural framework and polynomial spectral factorization
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行为框架和多项式谱分解中的卡尔曼-雅库博维奇-波波夫引理
DOI：
10.1109/cdc.1997.657753
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
H. Trentelman
中科院分区：
文献类型：
--
作者：
Geest van der Robert;H. Trentelman
经典的卡尔曼-雅库博维奇-波波夫引理提供了状态空间形式系统耗散率与线性矩阵不等式解之间的联系。本文导出了用高阶微分方程描述的线性系统的KYP引理。结果是用原始系数表示的LMI，其中提出了耗散率问题。随后，我们研究了多项式矩阵的耗散率与谱分解之间的联系。这使我们能够根据多项式矩阵系数中的LMI推导出多项式谱分解的新算法。
The classical Kalman-Yakubovich-Popov lemma provides a link between dissipativity of a system in state-space form and the solution to a linear matrix inequality. In this paper we derive the KYP lemma for linear systems described by higher-order differential equations. The result is an LMI in terms of the original coefficients in which the dissipativity problem is posed. Subsequently we study the connection between dissipativity and spectral factorization of polynomial matrices. This enables us to derive a new algorithm for polynomial spectral factorization in terms of an LMI in the coefficients of the polynomial matrix.