# On the Baer extension problem for multidimensional linear systems

Abstract : Within an algebraic analysis approach, the purpose of the paper is to constructively solve the following problem: given two fixed multidimensional linear systems $S_1$ and $S_2$, parametrize the multidimensional linear systems $S$ which contain $S_1$ as a subsystem and satisfy that $S/S_1$ is isomorphic to $S_2$. In order to study this problem, we use Baer's classical interpretation of the extension functor and give an explicit characterization and parametrization of the equivalence classes of multidimensional linear systems $S$ solving this problem. We then use these results to parametrize the equivalence classes of multidimensional linear systems $S$ which admit a fixed parametrizable subsystem $S_1$ and satisfy that $S/S_1$ is isomorphic to a fixed autonomous system $S_2$. We illustrate the main results by means of explicit examples of differential time-delay systems.
Keywords :
Type de document :
Rapport
[Research Report] RR-6307, INRIA. 2007, pp.43
Domaine :

Littérature citée [31 références]

https://hal.inria.fr/inria-00175272
Contributeur : Rapport de Recherche Inria <>
Soumis le : jeudi 27 septembre 2007 - 16:55:11
Dernière modification le : jeudi 11 janvier 2018 - 16:31:01
Document(s) archivé(s) le : mardi 21 septembre 2010 - 13:18:09

### Fichiers

RR-6307.pdf
Fichiers produits par l'(les) auteur(s)

### Identifiants

• HAL Id : inria-00175272, version 2

### Citation

Alban Quadrat, Daniel Robertz. On the Baer extension problem for multidimensional linear systems. [Research Report] RR-6307, INRIA. 2007, pp.43. 〈inria-00175272v2〉

### Métriques

Consultations de la notice

## 281

Téléchargements de fichiers