Minimal state-space realization in linear system theory: An overview
type: Item
instance of: scholarly article
title: Minimal state-space realization in linear system theory: An overview
zbMATH Open document ID: 0963.93008
DOI: 10.1016/S0377-0427(00)00341-1
published in: Journal of Computational and Applied Mathematics
publication date: 2000-11-20T00:00:00Z
review text: The paper is a complete survey of the minimal state-space realization problem for linear time-invariant systems. After a brief historical overview and an introduction to the domain, the paper focusses on some of the basic algorithms as Rosenbrock's procedure of reduction of nonminimal realizations or algorithms for minimal state-space realizations of impulse responses based on the block Hankel matrices; Silverman's algorithm as well as the celebrated algorithm of B. L. Ho are presented. Different approaches to the minimal partial realization problem are examined, as well as minimal realization of noisy measurements of the impulse response or minimal realization based on step response data. Related problems and extensions are discussed like rational approximation, model reduction, identification, positive linear systems, max-puls-algebraic models or multidimensional systems. A bibliography containing 61 titles gives a full information about the discussed topic.
reviewed by: Valeriu Prepeliţă
Mathematics Subject Classification ID: 93-02
Mathematics Subject Classification ID: 93B20
zbMATH DE Number: 1533140
zbMATH Keywords: survey
zbMATH Keywords: minimal state-space realization
zbMATH Keywords: impulse responses
zbMATH Keywords: partial realization
zbMATH Keywords: step response data
author: Bart De Schutter
describes a project that uses: SLICOT
MaRDI profile type: Publication
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Wikidata QID: Q127560938
full work available at URL: s0377-0427(00)00341-1
OpenAlex ID: W2109161029
description: scientific article; zbMATH DE number 1533140