Deformation and stability of triples of matrices
type: Item
instance of: scholarly article
title: Deformation and stability of triples of matrices
zbMATH Open document ID: 0873.93040
DOI: 10.1016/S0024-3795(96)00404-1
author: I. García-Planas
author: D. Magret
published in: Linear Algebra and its Applications
publication date: 1997-05-20T00:00:00Z
review text: For a linear dynamical system described by \(\dot x= Ax+Bu\), \(y=Cx\), \(x\in\mathbb{C}^n\), \(u\in\mathbb{C}^m\), \(y\in \mathbb{C}^p\), based on a result describing explicitly the orthogonal miniversal deformation of \((A,B,C)\), one shows that the structural stability of \((A,B,C)\) is equivalent with one of the following conditions, corresponding to a different relation among \(n\), \(m\) and \(p\): (a) \(n\leq \min(m,p):(A,B,C)\) has only infinite elementary divisors with exponent two. (b) \(m>p\), \(n\geq p\); \((A,B,C)\) has only column-minimal indices that are equal or differ by one unity, and infinitely many elementary divisors with exponent two. (c) \(p>m\), \(n\geq m:(A,B,C)\) has only row-minimal indices that are equal or differ by one unity, and infinitely many elementary divisors with exponent two.
reviewed by: Mihail Voicu
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93D20
Mathematics Subject Classification ID: 93B25
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 1000051
zbMATH Keywords: linear dynamical system
zbMATH Keywords: miniversal deformation
zbMATH Keywords: structural stability
zbMATH Keywords: elementary divisors
MaRDI profile type: Publication
cites work: ON MATRICES DEPENDING ON PARAMETERS
cites work: Structural stability of quadruples of matrices
cites work: Q3748420
cites work: Points of Continuity of the Kronecker Canonical Form
cites work: Q4744461
cites work: Q3222981
cites work: Invariance and system theory: algebraic and geometric aspects
cites work: Topological classification and structural stability of linear systems
description: scientific article; zbMATH DE number 1000051