A new two-step iterative method for optimal reduction of linear SISO systems
type: Item
instance of: scholarly article
title: A new two-step iterative method for optimal reduction of linear SISO systems
zbMATH Open document ID: 0881.93014
DOI: 10.1016/0016-0032(96)00049-X
author: Jyh-Haur Hwang
author: Chyi Hwang
published in: Journal of the Franklin Institute
publication date: 1998-01-27T00:00:00Z
review text: This paper discusses the model reduction problem of SISO systems. A strictly proper rational transfer function \(G_n\) of degree \(n\) is approximated by a strictly proper rational transfer function \(G_m\) of lower degree \(m<n\). The approximation criterion is to minimise \(\int_0^\infty e(t)^2dt\) where \(e(t)\) is the response of the system with transfer function \(G_n-G_m\) to an input with Laplace transform \(R(s)=s^{-l}\) where \(l=0\) or 1. The classical free parameters of the problem (the coefficients of the numerator and denominator of \(G_m\)) are replaced by the Routh stability parameters of the denominator and the coefficients of the numerator. Then stability of the approximant is guaranteed if these Routh parameters are subject to a simple positivity constraint. The solution of this constrained optimization problem is based on a gradient method. Explicit expressions for this gradient are derived. The iteration alternates between an update of the Routh parameters and an update of the numerator coefficients.
Mathematics Subject Classification ID: 93B11
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 90C31
zbMATH DE Number: 1060097
zbMATH Keywords: model reduction
zbMATH Keywords: linear systems
zbMATH Keywords: stability of the approximant
zbMATH Keywords: Routh parameters
zbMATH Keywords: constrained optimization
zbMATH Keywords: gradient method
reviewed by: Adhemar Bultheel
MaRDI profile type: Publication
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full work available at URL: 0016-0032(96)00049-x
OpenAlex ID: W1973534195
description: scientific article; zbMATH DE number 1060097