Numerical computation of a coprime factorization of a transfer function matrix
type: Item
instance of: scholarly article
title: Numerical computation of a coprime factorization of a transfer function matrix
zbMATH Open document ID: 0629.93027
DOI: 10.1016/0167-6911(87)90052-1
author: B. George
published in: Systems \& Control Letters
publication date: 1987-01-01T00:00:00Z
review text: The problem of computing a (right) coprime factorization \(N_ r(\lambda)D_ r^{-1}(\lambda)\) of a given rational transfer function matrix \(H(\lambda)=D_ L^{-1}(\lambda)N_ L(\lambda)\) has a well- known algebraic but not an efficient numerical solution. The authors reformulate this problem as a problem of constructing a minimal polynomial basis of the right nullspace of a matrix pencil \(\lambda\) B-A associated to the polynomial matrix \(P(\lambda)=[N_ L(\lambda),D_ L(\lambda)]\). This latter problem is solved by transformating \(\lambda\) B-A to a generalized Schur form of a pencil by numerically backward stable algorithms as analyzed in the first author's Ph.D. thesis. The complete algorithm is presented and illustrated by two numerical examples of coprime factorizations chosen from the literature.
Mathematics Subject Classification ID: 93B40
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 93B10
Mathematics Subject Classification ID: 93B25
zbMATH DE Number: 4025262
zbMATH Keywords: coprime factorization
zbMATH Keywords: rational transfer function matrix
zbMATH Keywords: minimal polynomial basis
zbMATH Keywords: matrix pencil
zbMATH Keywords: generalized Schur form
zbMATH Keywords: algorithm
MaRDI profile type: Publication
full work available at URL: 0167-6911(87)90052-1
OpenAlex ID: W2109184371
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description: scientific article; zbMATH DE number 4025262