Continued-fraction decomposition of linear systems in the state space
type: Item
instance of: scholarly article
title: Continued-fraction decomposition of linear systems in the state space
zbMATH Open document ID: 0627.93013
DOI: 10.1016/0167-6911(87)90007-7
author: R. H. Bishop
author: A. C. Antoulas
published in: Systems \& Control Letters
publication date: 1987-01-01T00:00:00Z
review text: The authors develop a continued fraction decomposition of formal matrix power series \(Z=A_ 1s^{-1}+...+A_ ts^{-t}+...\), \(A_ t\in k^{p\times m}\). The decomposition is interpreted as a certain feedback interconnection of linear systems. If Z is the transfer matrix of a reachable and observable linear system they show that each \(A_ t\) is uniquely associated with a subsystem in the interconnection, moreover a partitioning of the MacMillan degree and of the Kronecker indices is induced. This constitutes a continued fraction canonical form. The maximal (F,G)-invariant subspace contained in ker H can be nicely determined in terms of the decomposition. The results are compared with the decomposition proposed by \textit{P. A. Fuhrmann} [ibid. 3, 263-271 (1983; Zbl 0567.65020).
Mathematics Subject Classification ID: 93B10
Mathematics Subject Classification ID: 30B70
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93B20
Mathematics Subject Classification ID: 93B25
Mathematics Subject Classification ID: 93C35
zbMATH DE Number: 4020932
zbMATH Keywords: continued fraction decomposition
zbMATH Keywords: formal matrix power series
zbMATH Keywords: feedback interconnection
zbMATH Keywords: continued fraction canonical form
reviewed by: Achim Ilchmann
MaRDI profile type: Publication
full work available at URL: 0167-6911(87)90007-7
OpenAlex ID: W2064450009
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description: scientific article; zbMATH DE number 4020932