Parametrization of Contractive Block Operator Matrices and Passive Discrete-Time Systems期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Parametrization of Contractive Block Operator Matrices and Passive Discrete-Time Systems

Authors:	Yury M. Arlinskiĭ Seppo Hassi Henk S. V. de Snoo

Affiliation:	(1) Department of Mathematical Analysis, East Ukrainian National University, Kvartal Molodyozhny 20-A, UA-Lugansk, 91034, Ukraine;(2) Department of Mathematics and Statistics, University of Vaasa, P.O. Box 700, FIN-65101 Vaasa, Finland;(3) Department of Mathematics and Computing Science, University of Groningen, P.O. Box 800, NL-9700 AV Groningen, Netherland

Abstract:	Passive linear systems τ = have their transfer function ${Theta_{tau}(lambda) = D + lambda C{(I - lambda A)^{-1}}B}$ in the Schur class S . Using a parametrization of contractive block operators the transfer function ${Theta_{tau}(lambda)}$ is connected to the Sz.-Nagy–Foiaş characteristic function ${Phi_{A}(lambda)}$ of the contraction A. This gives a new aspect and some explicit formulas for studying the interplay between the system τ and the functions ${Theta_{tau}(lambda)}$ and ${Phi_{A}(lambda)}$ . The method leads to some new results for linear passive discrete-time systems. Also new proofs for some known facts in the theory of these systems are obtained. Dedicated to Eduard Tsekanovskiĭ on the occasion of his seventieth birthday This work was supported by the Research Institute for Technology at the University of Vaasa. The first author was also supported by the Academy of Finland (projects 212146, 117617) and the Dutch Organization for Scientific Research N.W.O. (B 61-553). Received: December 22, 2006. Revised: February 6, 2007.

Keywords:	KeywordHeading" >Mathematics Subject Classification (2000). Primary 47A45, 47A48, 47A56, 47N70 Secondary 93B15
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