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Canonical factorization of rational matrix functions. A note on a paper by P. Dewilde
- Source :
- Frazho, A E & Kaashoek, M A 2012, ' Canonical factorization of rational matrix functions. A note on a paper by P. Dewilde. ', Indagationes Mathematicae, vol. 23, no. 4, pp. 1154-1164 . https://doi.org/10.1016/j.indag.2012.09.001, Indagationes Mathematicae, 23(4), 1154-1164. Elsevier
- Publication Year :
- 2012
- Publisher :
- Elsevier BV, 2012.
-
Abstract
- 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. © 2012 Royal Dutch Mathematical Society (KWG).
- Subjects :
- Mathematics(all)
General Mathematics
Stein equation
Rational matrix functions
Operator theory
Unitary state
LU decomposition
law.invention
Algebra
LTI system theory
Riccati equation
Unit circle
Factorization
law
Canonical factorization
Unitary matrix functions
State space (physics)
State space realization
Toeplitz operators
Mathematics
Subjects
Details
- ISSN :
- 00193577
- Volume :
- 23
- Database :
- OpenAIRE
- Journal :
- Indagationes Mathematicae
- Accession number :
- edsair.doi.dedup.....7fc34277dc99c2e4d88f066828b2249c