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Minimal Degree Coprime Factorization of Rational Matrices

Oara, C. and Varga, A. (1999) Minimal Degree Coprime Factorization of Rational Matrices. SIAM Journal on Matrix Analysis and Applications, 21 (1), pp. 245-278.



Given a rational matrix G with complex coefficients and a domain Gamma in the closed complex plane, both arbitrary, we develop a complete theory of coprime factorizations of G over Gamma, with denominators of McMillan degree as small as possible. The main tool is a general pole displacement theorem which gives conditions for an invertible rational matrix to dislocate by multiplication a part of the poles of G. We apply this result to obtain the parametrized class of all coprime factorizations over Gamma with denominators of minimal McMillan degree nb-the number of poles G outside Gamma. Spezific choices of the parameters and of Gamma allow us to determine coprime factorizations, as for instance, with polynomial, proper, or stable factors. Further, we consider the case in which the denominator has a certain symmetry, namely it is J all-pass with respect either to the imaginary axis or to the unit circle. We give necessary and sufficient solvability conditions for the problem of coprime factorization with J all-pass denominator of McMillan degree nb and, when a solution exists, we give a construction of the class of coprime factors. When no such solution exists, we discuss the existence of, and give solutions to, comprime factorizations with J all-pass denominators of minimal McMillan degree (< nb). All the developments are carried out in terms of descriptor realizations associated with rational matrices, leading to explicit and computationally efficient formulas.

Item URL in elib:https://elib.dlr.de/3507/
Document Type:Article
Additional Information:LIDO-Berichtsjahr=1999,
Title:Minimal Degree Coprime Factorization of Rational Matrices
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Oara, C.Univ. Polytechnica BucharestUNSPECIFIED
Journal or Publication Title:SIAM Journal on Matrix Analysis and Applications
Open Access:Yes
Gold Open Access:No
In ISI Web of Science:No
Page Range:pp. 245-278
Keywords:rational matrices, coprime factorizations, J all-pass, descriptor realizations, numerical algorithms
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:Aircraft Research (old)
DLR - Research area:Aeronautics
DLR - Program:L AR - Aircraft Research
DLR - Research theme (Project):L - Flexible Aircraft (old)
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Robotics and Mechatronics (until 2012) > Institut für Robotik und Systemdynamik
Deposited By: DLR-Beauftragter, elib
Deposited On:16 Sep 2005
Last Modified:31 Jul 2019 19:14

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