A note on the existence of positive realizations
type: Item
instance of: scholarly article
title: A note on the existence of positive realizations
zbMATH Open document ID: 1060.93030
author: Alessandro Astolfi
author: Patrizio Colaneri
published in: Linear Algebra and its Applications
publication date: 2004-11-18T00:00:00Z
review text: This paper contains the following result: Let \(G(s)\) be a strictly proper rational transfer function of degree \(n\). Then (A) and (B) are equivalent: (A) \(G(s)\) admits an asymptotically stable minimal positive diagonal realization. (B) \(G(s)\) is asymptotically stable, minimum phase and the poles and zeros of \(G(s)\) are real and interlaced. The authors also prove that (A) and (B) are equivalent to a statement about two submatrices of the infinite Hankel matrix associated to \(G(s)\). A similar result is given for a discrete-time transfer function. The above result is also extended to possibly unstable transfer functions in continuous time. The above results are applied to a number of other cases as well, leading for instance to the following corollary: Let \(d(s)\) be a monic polynomial with all real roots. Then \(G(s):=d(s)^{-1}\) admits a minimal positive realization. The well written paper ends with a number of examples and an adequate list of references.
Mathematics Subject Classification ID: 93B20
zbMATH DE Number: 2116541
zbMATH Keywords: positive systems
zbMATH Keywords: Hankel matrices
zbMATH Keywords: minimal realization
zbMATH Keywords: diagonal
zbMATH Keywords: interlaced poles and zeros
reviewed by: Johannes W. Nieuwenhuis
MaRDI profile type: Publication
full work available at URL: j.laa.2004.06.015
OpenAlex ID: W2043756932
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DOI: 10.1016/J.LAA.2004.06.015
description: scientific article; zbMATH DE number 2116541