A canonical parametrization of the Kronecker form of a matrix pencil
type: Item
instance of: scholarly article
title: A canonical parametrization of the Kronecker form of a matrix pencil
zbMATH Open document ID: 0826.93009
DOI: 10.1016/0005-1098(94)00111-U
author: J. M. Berg
author: Harry G. Kwatny
published in: Automatica
publication date: 1995-11-27T00:00:00Z
review text: The authors give an algorithm based on a theorem of \textit{A. Tannenbaum} [Invariance and system theory: Algebraic and geometric aspects; Lect. Notes Math. 845 (1981; Zbl 0456.93001)] for computing a versal deformation of the Kronecker canonical form of a matrix pencil. The deformation seen as a mapping from the manifold of parameters to the manifold of matrix pencils has to be transversal at the canonical pencil to the orbit containing the canonical pencil under the action of a pencil (composed of elements of the linear group) through conjugation. The deformation contains as few parameters as possible. The computations are carried out in the thesis of the first author [Unfolding of singular pencils with applications to control systems. PhD thesis, Drexel University (1992)]but the results are given here. They are valid only if the finite zero eigenvalues of the pencil are distinct.
Mathematics Subject Classification ID: 93B10
Mathematics Subject Classification ID: 15A22
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 93B29
Mathematics Subject Classification ID: 93B60
Mathematics Subject Classification ID: 57S25
Mathematics Subject Classification ID: 93C05
zbMATH DE Number: 777943
zbMATH Keywords: algorithm
zbMATH Keywords: versal deformation
zbMATH Keywords: Kronecker canonical form
zbMATH Keywords: matrix pencil
zbMATH Keywords: zero
reviewed by: A. Akutowicz
MaRDI profile type: Publication
cites work: A nine-fold canonical decomposition for linear systems
cites work: ON MATRICES DEPENDING ON PARAMETERS
cites work: Q4744562
cites work: Q3729587
cites work: The Set of 2-by-3 Matrix Pencils — Kronecker Structures and Their Transitions under Perturbations
cites work: On strict system equivalence and similarity†
cites work: Q3254327
cites work: Q3962198
cites work: Q4066911
cites work: Minimality of descriptor representations under external equivalence
cites work: Poles and zeros of linear multivariable systems : a survey of the algebraic, geometric and complex-variable theory
cites work: Structural Invariants of Linear Multivariable Systems
cites work: Transformations of matrix pencils and implications in linear systems theory
cites work: Structural properties of linear dynamical systems
cites work: Invariance and system theory: algebraic and geometric aspects
cites work: The singular pencil of a linear dynamical system†
cites work: The computation of Kronecker's canonical form of a singular pencil
cites work: The generalized eigenstructure problem in linear system theory
cites work: Q4527707
cites work: A generalized state-space for singular systems
cites work: Invariants and Canonical Forms under Dynamic Compensation
cites work: Feedback invariants of linear multivariable systems
full work available at URL: 0005-1098(94)00111-u
OpenAlex ID: W1993409353
description: scientific article; zbMATH DE number 777943