1. Canonical factorization of rational matrix functions. A note on a paper by P. Dewilde
- Author
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Arthur E. Frazho, Marinus A. Kaashoek, and Mathematics
- 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 - 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).
- Published
- 2012