Canonical factorization of rational matrix functions. A note on a paper by P. Dewilde

A left canonical factorization theorem for rational matrix functions relative to the unit circle is presented. The result is a time invariant version of a recent strict LU factorization theorem for certain semi-separable operators, due to Dewilde (2012) [6]. Explicit formulas for the factors are als...

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Bibliographic Details
Published inIndagationes mathematicae Vol. 23; no. 4; pp. 1154 - 1164
Main Authors Frazho, A.E., Kaashoek, M.A.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2012
Subjects
Canonical factorization
Rational matrix functions
Riccati equation
State space realization
Stein equation
Toeplitz operators
Unitary matrix functions
Stein equation
Rational matrix functions
Canonical factorization
Unitary matrix functions
Toeplitz operators
Riccati equation
State space realization
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Summary:A left canonical factorization theorem for rational matrix functions relative to the unit circle is presented. The result is a time invariant version of a recent strict LU factorization theorem for certain semi-separable operators, due to Dewilde (2012) [6]. Explicit formulas for the factors are also given. The theorem is proved, first by using the state space method of Dewilde (2012) [6], and next by using an operator theory approach. In both cases the main part of the proof concerns rational matrix functions that are unitary on the unit circle.
ISSN:0019-3577
1872-6100
DOI:10.1016/j.indag.2012.09.001