Local Wiener--Hopf factorization and indices over arbitrary fields
type: Item
instance of: scholarly article
title: Local Wiener--Hopf factorization and indices over arbitrary fields
zbMATH Open document ID: 1157.47015
author: A. Amparan
author: S. Marcaida
author: Ion Zaballa
published in: Linear Algebra and its Applications
publication date: 2009-02-25T00:00:00Z
review text: Comprising four sections and two appendices, the paper gives generalizations to arbitrary fields of the usual Wiener--Hopf equivalence of complex valued rational matrix functions. Also, the local Wiener--Hopf factorization indices introduced in [Linear Algebra Appl.\ 425, No~2--3, 757--775 (2007; Zbl 1126.93020)] are proved to form a complete system of invariants for this equivalence relation. The first two sections present a detailed history of the topic and introduce some necessary definitions. In the third section, the local Wiener--Hopf equivalence of non-singular rational matrices over an arbitrary field with respect with two subsets in the set of all maximal ideals of the ring of polynomials with coefficients in the considered field is defined. The main results are that the factorization indices form a complete system of invariants, and, under certain conditions, every non-singular polynomial matrix is equivalent to a diagonal matrix. In the fourth section, the obtained results are applied to linear control systems. Also is proved here that any controllable pair can be reduced by feedback equivalence to a reduced form similar to the Brunovski canonical form. The paper concludes with two appendices which present the basic Wiener--Hopf factorization theorem over the complex field, and the generalization procedure to arbitrary fields. Also, the left Wiener--Hopf equivalence of rational matrix functions is analysed
reviewed by: Ilie Valuşescu
Mathematics Subject Classification ID: 47A68
Mathematics Subject Classification ID: 93B25
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93C05
zbMATH DE Number: 5518782
zbMATH Keywords: Wiener-Hopf factorization indices
zbMATH Keywords: local rings
zbMATH Keywords: rational matrices
MaRDI profile type: Publication
full work available at URL: j.laa.2008.10.001
OpenAlex ID: W2089324853
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DOI: 10.1016/J.LAA.2008.10.001
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description: scientific article; zbMATH DE number 5518782