Characterizations of rectangular (para)-unitary rational functions

• Autorzy: Alpay D. , Jorgensen P. , Lewkowicz I.

Identyfikatory

DOI

10.7494/OpMath.2016.36.6.695

• Języki publikacji: EN

Abstrakty

EN

We here present three characterizations of not necessarily causal, rational functions which are (co)-isometric on the unit circle: (i) through the realization matrix of Schur stable systems, (ii) the Blaschke-Potapov product, which is then employed to introduce an easy-to-use description of all these functions with dimensions and McMillan degree as parameters, (iii) through the (not necessarily reducible) Matrix Fraction Description (MFD). In cases (ii) and (iii) the poles of the rational functions involved may be anywhere in the complex plane, but the unit circle (including both zero and infinity). A special attention is devoted to exploring the gap between the square and rectangular cases.

Słowa kluczowe

EN

isometry; coisometry; lossless; all-pass; realization; gramians; matrix fraction description; Blaschke-Potapov product

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2016
• Tom: Vol. 36, no. 6
• Strony: 695--716
• Opis fizyczny: Bibliogr. 48 poz,

Twórcy

autor

Alpay D.

• Department ol Mathematics Ben Gurion University ol the Negev P.O.B. 653, Be'er Sheva 84105, Israel

autor

Jorgensen P.

• Department of Mathematics 14 MLH, The University of Iowa Iowa City, IA 52242-1419, USA

autor

Lewkowicz I.

• Department of Electrical Engineering Ben Gurion University of the Negev P.O.B. 653, Be'er Sheva 84105, Israel

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Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.