An algorithm for coprime matrix fraction description using Sylvester matrices
type: Item
instance of: scholarly article
title: An algorithm for coprime matrix fraction description using Sylvester matrices
zbMATH Open document ID: 0886.65042
DOI: 10.1016/S0024-3795(96)00636-2
published in: Linear Algebra and its Applications
publication date: 1998-04-13T00:00:00Z
review text: The problem of coprime matrix fraction description (MFD) of transfer function matrices is considered: given a \(p \times q\) transfer function matrix \(H(z)\) with a left MFD \(A^{-1}(z)B(z)\), find a right coprime MFD \(N(z)M^{-1}(z)\), where \(A(z)\), \(B(z)\), \(N(z)\) and \(M(z)\) are \(p \times p\), \(p \times q\), \(p \times q\) and \(q \times q\) polynomial matrices respectively, \(A(z) = \sum_{k=0}^{a} A_k z^{a-k}\), \(B(z) = \sum_{k=0}^{b} B_k z^{b-k}\), \(N(z) = \sum_{k=0}^{n} N_k z^{n-k}\), \(M(z) = \sum_{k=0}^{m} M_k z^{m-k}\). The problem then reduces to finding \(N_k\), \(0 \leq k \leq n\), and \(M_k\), \(0 \leq k \leq m\), which is equivalent to solving \(S_{m,n}(B,A)X=0\), where \(S_{m,n}\) is the Sylvester resultant matrix of \(A(z)\) and \(B(z)\). The authors explore the properties of \(S_{m,n}(B,A)\) in order to determine the smallest permissible values for \(m\) and \(n\), and propose an algorithm for the computation of matrices \(X\) which lead to coprime polynomial factorization. The algorithm is based on singular value decomposition and therefore avoids problems of numerical ill-conditioning. Numerical examples illustrate the advantages of the proposed method. The same approach can be used to compute column reduced equivalents of polynomial matrices.
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15A54
zbMATH DE Number: 1083212
zbMATH Keywords: polynomial matrices
zbMATH Keywords: Sylvester matrix
zbMATH Keywords: coprime polynomial factorization
zbMATH Keywords: singular value decomposition
zbMATH Keywords: coprime matrix fraction description
zbMATH Keywords: transfer function matrices
zbMATH Keywords: numerical examples
author: J. C. Basilio
author: Basil Kouvaritakis
reviewed by: Neli Dimitrova
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1083212