Computation of balanced realisation approximations of delay systems
type: Item
instance of: scholarly article
title: Computation of balanced realisation approximations of delay systems
zbMATH Open document ID: 0962.93030
DOI: 10.1016/S0947-3580(99)70170-6
author: James Lam
published in: European Journal of Control
publication date: 2000-01-04T00:00:00Z
review text: Delay systems with transfer functions of the form \(G(s)= e^{-sT}g(s)\) are considered, where \(T>0\) and \(g(s)\) is a scalar strictly proper rational function. One gives numerically reliable algorithms for the computation of a finite-dimensional balanced realization of the stable part of \(G(s)\). Some properties of the Hankel singular values are emphasized, including an upper bound and their asymptotic behaviour; knowledge of this behaviour leads to a reduction in computational effort. An algorithm is proposed for the determination of the Hankel singular values as the zero crossings of a determinant function. The accuracy of these calculations is improved by employing matrix transformations and scaling. Another algorithm gives the initial values of the Schmidt vectors. These results are used in an algorithm which provides approximation of delay based on (Ober type) balanced realization. Some numerical examples illustrate the efficiency of these algorithms in the computation of the balanced realization approximation.
Mathematics Subject Classification ID: 93B40
Mathematics Subject Classification ID: 93B11
Mathematics Subject Classification ID: 34K35
Mathematics Subject Classification ID: 93B20
Mathematics Subject Classification ID: 93B60
zbMATH DE Number: 1382831
zbMATH Keywords: model reduction
zbMATH Keywords: delay systems
zbMATH Keywords: balanced realization
zbMATH Keywords: Hankel singular values
reviewed by: Valeriu Prepeliţă
MaRDI profile type: Publication
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full work available at URL: s0947-3580(99)70170-6
OpenAlex ID: W2091450142
description: scientific article; zbMATH DE number 1382831