Title :

On the Ore extension ring of differential time-varying delay operators

Author(s) :

Quadrat, Alban [Auteur]
Institut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG (UMR_7586)]
OUtils de Résolution Algébriques pour la Géométrie et ses ApplicatioNs [OURAGAN]
Ushirobira, Rosane [Auteur]
Finite-time control and estimation for distributed systems [VALSE]

Book title :

Accounting for Constraints in Delay Systems, Advances in Delays and Dynamics (ADD), volume 12, Springer, pp. 87-107

Publisher :

Springer

Publication date :

2022-04-03

ISBN :

978-3-030-89014-8

HAL domain(s) :

Sciences de l'ingénieur [physics]/Automatique / Robotique
Informatique [cs]/Calcul formel [cs.SC]
Mathématiques [math]/Anneaux et algèbres [math.RA]
Mathématiques [math]/Algèbres d'opérateurs [math.OA]
Mathématiques [math]/Optimisation et contrôle [math.OC]

English abstract : [en]

In this work, we propose an algebraic method to study linear differential time-varying delay (DTVD) systems. Our goal is to give an effective construction of the ring of DTVD operators as an Ore extension, thanks to the ...
Show more >In this work, we propose an algebraic method to study linear differential time-varying delay (DTVD) systems. Our goal is to give an effective construction of the ring of DTVD operators as an Ore extension, thanks to the concept of skew polynomial rings developed by Ore in the 30s. Some algebraic properties of the DTVD operators ring are analyzed, such as its Noetherianity, its homological and Krull dimensions, and the existence of Gröbner bases, all given in terms of the time-varying delay function. The algebraic analysis framework for linear systems theory allows us to study linear DTVD systems and essential properties such as the existence of autonomous elements, controllability, parametrizability, flatness, etc., through methods coming from module theory, homological algebra, and constructive algebra.Show less >

Language :

Anglais

Audience :

Internationale

Popular science :

Non

Collections :

• Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL