Algebraic analysis for the Ore extension ring of differential time-varying delay operators

Alban Quadrat 1 Rosane Ushirobira 1
1 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : As far as we know, there is no algebraic (polynomial) approach for the study of linear differential time-delay systems in the case of a (sufficiently regular) time-varying delay. Based on the concept of skew polynomial rings developed by Ore in the 30s, the purpose of this paper is to construct the ring of differential time-delay operators as an Ore extension and to analyze its properties. Classical algebraic properties of this ring, such as noetherianity, its homological and Krull dimensions and the existence of Gröbner bases, are characterized in terms of the time-varying delay function. In conclusion, the algebraic analysis approach to linear systems theory allows us to study linear differential time-varying delay systems (e.g. existence of autonomous elements, controllability, parametrizability, flatness, behavioral approach) through methods coming from module theory, homological algebra and constructive algebra.
Keywords : Computer algebra
Type de document :
Communication dans un congrès
22nd International Symposium on Mathematical Theory of Networks and Systems (MTNS), Jul 2016, Minneapolis, United States. 22nd International Symposium on Mathematical Theory of Networks and Systems (MTNS), pp.8, 2016, 〈https://sites.google.com/a/umn.edu/mtns-2016/〉
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Contributeur : Alban Quadrat <>
Soumis le : jeudi 29 décembre 2016 - 18:05:28
Dernière modification le : jeudi 11 janvier 2018 - 06:27:32
Document(s) archivé(s) le : mardi 21 mars 2017 - 00:33:25

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Alban Quadrat, Rosane Ushirobira. Algebraic analysis for the Ore extension ring of differential time-varying delay operators. 22nd International Symposium on Mathematical Theory of Networks and Systems (MTNS), Jul 2016, Minneapolis, United States. 22nd International Symposium on Mathematical Theory of Networks and Systems (MTNS), pp.8, 2016, 〈https://sites.google.com/a/umn.edu/mtns-2016/〉. 〈hal-01415256〉

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