Comptes Rendus
Partial Differential Equations/Optimal Control
Controllability for a class of reaction–diffusion systems: the generalized Kalman's condition
[Contrôlabilité d'une classe de systèmes réaction–diffusion : la condition de Kalman généralisée]
Comptes Rendus. Mathématique, Volume 345 (2007) no. 10, pp. 543-548.

Dans cette Note, on étudie la contrôlabilité d'une classe de systèmes paraboliques de la forme Yt=(DΔ+A)Y+Bχωu avec des conditions de Dirichlet sur le bord d'un domaine borné Ω, où ωΩ est un sous-domaine. Ici D,AL(Rn), BL(Rm;Rn) et on montre que la condition algébrique de Kalman s'étend à de tels systèmes.

In this Note, we study the controllability of a class of parabolic systems of the form Yt=(DΔ+A)Y+Bχωu with Dirichlet conditions on the boundary of a bounded domain Ω, where ωΩ is a subdomain. Here D,AL(Rn), BL(Rm;Rn) and we prove that the algebraic Kalman condition extends to such systems.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.10.023

Farid Ammar-Khodja 1 ; Assia Benabdallah 2 ; Cédric Dupaix 1 ; Manuel González-Burgos 3

1 Laboratoire de mathématiques UMR 6623, Université de Franche-Comté, 16, route de Gray, 25030 Besançon cedex, France
2 CMI-LATP, UMR 6632, Université de Provence, technopôle Château-Gombert, 39, rue F. Joliot-Curie, 13453 Marseille cedex 13, France
3 Dpto. de Ecuaciones Diferentiales y Análisis Numérico, Universidad Sevilla, Aptdo. 1160, 41080 Sevilla, Spain
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     title = {Controllability for a class of reaction{\textendash}diffusion systems: the generalized {Kalman's} condition},
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Farid Ammar-Khodja; Assia Benabdallah; Cédric Dupaix; Manuel González-Burgos. Controllability for a class of reaction–diffusion systems: the generalized Kalman's condition. Comptes Rendus. Mathématique, Volume 345 (2007) no. 10, pp. 543-548. doi : 10.1016/j.crma.2007.10.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.10.023/

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