id,collection,Type de document,Titre,Auteur(s),Titre de la manifestation scientifique,Ville,Pays,Date de début de la manifestation scientifique,Titre de l'ouvrage,Date de publication,Mot(s)-clé(s) en anglais,Discipline(s) HAL,Résumé en anglais,Langue,Article revu par les pairs,Audience,Vulgarisation,Projet ANR
"08ef0b1d-37ce-400a-b964-099089332cf5","20.500.12210/28","Communication dans un congrès avec actes","Algebraic analysis for the Ore extension ring of differential time-varying delay operators","Quadrat, Alban||Ushirobira, Rosane","22nd International Symposium on Mathematical Theory of Networks and Systems (MTNS)","Minneapolis","Etats-Unis d'Amérique","2016-07-12","22nd International Symposium on Mathematical Theory of Networks and Systems (MTNS)","2016-07","Computer algebra","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]","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.","Anglais","Oui","Internationale","Non","Systèmes multidimensionnels, digression sur la stabilité"
