Pole-zero representation of descriptor systems
type: Item
instance of: scholarly article
title: Pole-zero representation of descriptor systems
zbMATH Open document ID: 0838.93031
DOI: 10.1016/0005-1098(94)00176-J
author: Pradeep Misra
author: Vassilis L. Syrmos
author: Paul van Dooren
published in: Automatica
publication date: 1996-06-04T00:00:00Z
review text: An algorithm for computing the poles and zeros of a regular descriptor system is given. The system is described by \[ \begin{cases} E\dot x & = Ax+ bu\\ y & = cx+ du,\end{cases} \] where \(\text{det}(\lambda E- A)\neq 0\). It is assumed that the system is irreducible (that is, it has no finite or infinite uncontrollable and/or unobservable modes). The algorithm for computing the poles consists of transforming the matrix pencil \((A- \lambda E)\) into the form \[ \left[\begin{matrix} A_1- \lambda E_1 & *\\ 0 & D(\lambda)\end{matrix}\right] \] by means of orthogonal transformations, where \(E_1\) is nonsingular, and \(D(\lambda)\) is upper triangular with constant diagonal elements. The poles then are the generalized eigenvalues of the pair \((E_1, A_1)\). The same algorithm applied to the matrix pencil \[ \left[\begin{matrix} A- \lambda E & b\\ c & d\end{matrix} \right] \] gives the zeros. Since the algorithm involves only orthogonal transformations, the results are numerically stable as illustrated by examples.
Mathematics Subject Classification ID: 93B60
Mathematics Subject Classification ID: 93B40
Mathematics Subject Classification ID: 15A22
zbMATH DE Number: 797335
zbMATH Keywords: transfer function
zbMATH Keywords: poles
zbMATH Keywords: zeros
zbMATH Keywords: descriptor system
zbMATH Keywords: matrix pencil
zbMATH Keywords: orthogonal transformations
reviewed by: M. Erol Sezer
MaRDI profile type: Publication
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Wikidata QID: Q127247433
full work available at URL: 0005-1098(94)00176-j
OpenAlex ID: W2093139703
description: scientific article; zbMATH DE number 797335