The algebraic structure of delay-differential systems: a behavioral perspective

Heide Glüsing-Lüerssen; Paolo Vettori; Sandro Zampieri

Kybernetika (2001)

  • Volume: 37, Issue: 4, page [397]-426
  • ISSN: 0023-5954

Abstract

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This paper presents a survey on the recent contributions to linear time- invariant delay-differential systems in the behavioral approach. In this survey both systems with commensurate and with noncommensurate delays will be considered. The emphasis lies on the investigation of the relationship between various systems descriptions. While this can be understood in a completely algebraic setting for systems with commensurate delays, this is not the case for systems with noncommensurate delays. In the study of this class of systems functional analytic methods need to be introduced and general convolutional equations have to be incorporated. Whenever it is possible, the results will be linked to the relevant control theoretic notions.

How to cite

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Glüsing-Lüerssen, Heide, Vettori, Paolo, and Zampieri, Sandro. "The algebraic structure of delay-differential systems: a behavioral perspective." Kybernetika 37.4 (2001): [397]-426. <http://eudml.org/doc/33544>.

@article{Glüsing2001,
abstract = {This paper presents a survey on the recent contributions to linear time- invariant delay-differential systems in the behavioral approach. In this survey both systems with commensurate and with noncommensurate delays will be considered. The emphasis lies on the investigation of the relationship between various systems descriptions. While this can be understood in a completely algebraic setting for systems with commensurate delays, this is not the case for systems with noncommensurate delays. In the study of this class of systems functional analytic methods need to be introduced and general convolutional equations have to be incorporated. Whenever it is possible, the results will be linked to the relevant control theoretic notions.},
author = {Glüsing-Lüerssen, Heide, Vettori, Paolo, Zampieri, Sandro},
journal = {Kybernetika},
keywords = {delay-differential system; algebraic methods; general convolution equations; noncommensurate delays; delay-differential systems; behavioral approach; delay-differential system; algebraic methods; general convolution equations; noncommensurate delays; delay-differential systems; behavioral approach},
language = {eng},
number = {4},
pages = {[397]-426},
publisher = {Institute of Information Theory and Automation AS CR},
title = {The algebraic structure of delay-differential systems: a behavioral perspective},
url = {http://eudml.org/doc/33544},
volume = {37},
year = {2001},
}

TY - JOUR
AU - Glüsing-Lüerssen, Heide
AU - Vettori, Paolo
AU - Zampieri, Sandro
TI - The algebraic structure of delay-differential systems: a behavioral perspective
JO - Kybernetika
PY - 2001
PB - Institute of Information Theory and Automation AS CR
VL - 37
IS - 4
SP - [397]
EP - 426
AB - This paper presents a survey on the recent contributions to linear time- invariant delay-differential systems in the behavioral approach. In this survey both systems with commensurate and with noncommensurate delays will be considered. The emphasis lies on the investigation of the relationship between various systems descriptions. While this can be understood in a completely algebraic setting for systems with commensurate delays, this is not the case for systems with noncommensurate delays. In the study of this class of systems functional analytic methods need to be introduced and general convolutional equations have to be incorporated. Whenever it is possible, the results will be linked to the relevant control theoretic notions.
LA - eng
KW - delay-differential system; algebraic methods; general convolution equations; noncommensurate delays; delay-differential systems; behavioral approach; delay-differential system; algebraic methods; general convolution equations; noncommensurate delays; delay-differential systems; behavioral approach
UR - http://eudml.org/doc/33544
ER -

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