On a homeomorphism between orbit spaces of linear systems and matrix polynomials

The orbit space of controllable systems under system similarity and the orbit space of matrix polynomials with determinant degree equal to the order of the state matrix under right equivalence are proved to be homeomorphic when the quotient compact–open topology is considered in the latter. As a con...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 436; no. 6; pp. 1664 - 1682
Main Authors Marcaida, S., Zaballa, I.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 15.03.2012
Elsevier
Subjects
Algebra
Compact-open topology
Control systems
Controllability
Exact sciences and technology
Invariant factor
Linear and multilinear algebra, matrix theory
Mathematics
Matrix polynomials
Perturbation
Realizations
Sciences and techniques of general use
Wiener-Hopf indices
Compact-open topology
Wiener-Hopf indices
Invariant factor
Control systems
Controllability
Perturbation
Realizations
Matrix polynomials
Invariant
Polynomial matrix
Similarity
Control system
Topology
Wiener Hopf method
Linear system
Homeomorphism
Matrix polynomial
Quotient
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Summary:The orbit space of controllable systems under system similarity and the orbit space of matrix polynomials with determinant degree equal to the order of the state matrix under right equivalence are proved to be homeomorphic when the quotient compact–open topology is considered in the latter. As a consequence, the variation of the finite and left Wiener–Hopf structures under small perturbations of matrix polynomials with fixed degree for their determinants is described.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2011.03.022