Algebraic analysis for the Ore extension ...
Type de document :
Communication dans un congrès avec actes
Titre :
Algebraic analysis for the Ore extension ring of differential time-varying delay operators
Auteur(s) :
Quadrat, Alban [Auteur]
Non-Asymptotic estimation for online systems [NON-A]
Ushirobira, Rosane [Auteur]
Non-Asymptotic estimation for online systems [NON-A]
Non-Asymptotic estimation for online systems [NON-A]
Ushirobira, Rosane [Auteur]
Non-Asymptotic estimation for online systems [NON-A]
Titre de la manifestation scientifique :
22nd International Symposium on Mathematical Theory of Networks and Systems (MTNS)
Ville :
Minneapolis
Pays :
Etats-Unis d'Amérique
Date de début de la manifestation scientifique :
2016-07-12
Titre de l’ouvrage :
22nd International Symposium on Mathematical Theory of Networks and Systems (MTNS)
Date de publication :
2016-07
Mot(s)-clé(s) en anglais :
Computer algebra
Discipline(s) HAL :
Mathématiques [math]/Anneaux et algèbres [math.RA]
Mathématiques [math]/Algèbres d'opérateurs [math.OA]
Mathématiques [math]/Optimisation et contrôle [math.OC]
Informatique [cs]/Calcul formel [cs.SC]
Mathématiques [math]/Algèbres d'opérateurs [math.OA]
Mathématiques [math]/Optimisation et contrôle [math.OC]
Informatique [cs]/Calcul formel [cs.SC]
Résumé en anglais : [en]
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 ...
Lire la suite >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.Lire moins >
Lire la suite >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.Lire moins >
Langue :
Anglais
Comité de lecture :
Oui
Audience :
Internationale
Vulgarisation :
Non
Collections :
Source :
Fichiers
- https://hal.inria.fr/hal-01415256/document
- Accès libre
- Accéder au document
- https://hal.inria.fr/hal-01415256/document
- Accès libre
- Accéder au document
- https://hal.inria.fr/hal-01415256/document
- Accès libre
- Accéder au document
- document
- Accès libre
- Accéder au document
- Ore_extension_ring.pdf
- Accès libre
- Accéder au document