A generalization of the Kalman rank condition for time-dependent coupled linear parabolic systems

In this paper we present a generalization of the Kalman rank condition for linear ordinary differential systems to the case of systems of n coupled parabolic equations (posed in the time interval (0,T) with T > 0) where the coupling matrices A and B depend on the time variable t . To be precise,...

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Autores: Ammar-Khodja, Farid, Benabdallah, Assia, Dupaix, Cédric, González Burgos, Manuel
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2009
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/48942
Acceso en línea:http://hdl.handle.net/11441/48942
https://doi.org/10.7153/dea-01-24
Access Level:acceso abierto
Palabra clave:Kalman condition
Control
Observability
Carleman estimates
Parabolic systems
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spelling A generalization of the Kalman rank condition for time-dependent coupled linear parabolic systemsAmmar-Khodja, FaridBenabdallah, AssiaDupaix, CédricGonzález Burgos, ManuelKalman conditionControlObservabilityCarleman estimatesParabolic systemsIn this paper we present a generalization of the Kalman rank condition for linear ordinary differential systems to the case of systems of n coupled parabolic equations (posed in the time interval (0,T) with T > 0) where the coupling matrices A and B depend on the time variable t . To be precise, we will prove that the Kalman rank condition rank [A|B](t0) = n, with t0 ∈ [0,T], is a sufficient condition (but not necessary) for obtaining the exact controllability to the trajectories of the considered parabolic system. In the case of analytic matrices A and B (and, in particular, constant matrices), we will see that the Kalman rank condition characterizes the controllability properties of the system. When the matrices A and B are constant and condition rank [A|B] = n holds, we will be able to state a Carleman inequality for the corresponding adjoint problem.Agence Nationale de la rechercheDirección General de Enseñanza SuperiorEle-MathEcuaciones Diferenciales y Análisis NuméricoFQM131: Ec.diferenciales,Simulación Num.y Desarrollo SoftwareAgence Nationale de la Recherche. FranceDirección General de Enseñanza Superior. España2009info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/48942https://doi.org/10.7153/dea-01-24reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésDifferential Equations & Application, 1 (3), 427-457.ANR-07-JCJC-0139-01MTM2006-07932http://files.ele-math.com/articles/dea-01-24.pdfinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/489422026-06-17T12:51:07Z
dc.title.none.fl_str_mv A generalization of the Kalman rank condition for time-dependent coupled linear parabolic systems
title A generalization of the Kalman rank condition for time-dependent coupled linear parabolic systems
spellingShingle A generalization of the Kalman rank condition for time-dependent coupled linear parabolic systems
Ammar-Khodja, Farid
Kalman condition
Control
Observability
Carleman estimates
Parabolic systems
title_short A generalization of the Kalman rank condition for time-dependent coupled linear parabolic systems
title_full A generalization of the Kalman rank condition for time-dependent coupled linear parabolic systems
title_fullStr A generalization of the Kalman rank condition for time-dependent coupled linear parabolic systems
title_full_unstemmed A generalization of the Kalman rank condition for time-dependent coupled linear parabolic systems
title_sort A generalization of the Kalman rank condition for time-dependent coupled linear parabolic systems
dc.creator.none.fl_str_mv Ammar-Khodja, Farid
Benabdallah, Assia
Dupaix, Cédric
González Burgos, Manuel
author Ammar-Khodja, Farid
author_facet Ammar-Khodja, Farid
Benabdallah, Assia
Dupaix, Cédric
González Burgos, Manuel
author_role author
author2 Benabdallah, Assia
Dupaix, Cédric
González Burgos, Manuel
author2_role author
author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
FQM131: Ec.diferenciales,Simulación Num.y Desarrollo Software
Agence Nationale de la Recherche. France
Dirección General de Enseñanza Superior. España
dc.subject.none.fl_str_mv Kalman condition
Control
Observability
Carleman estimates
Parabolic systems
topic Kalman condition
Control
Observability
Carleman estimates
Parabolic systems
description In this paper we present a generalization of the Kalman rank condition for linear ordinary differential systems to the case of systems of n coupled parabolic equations (posed in the time interval (0,T) with T > 0) where the coupling matrices A and B depend on the time variable t . To be precise, we will prove that the Kalman rank condition rank [A|B](t0) = n, with t0 ∈ [0,T], is a sufficient condition (but not necessary) for obtaining the exact controllability to the trajectories of the considered parabolic system. In the case of analytic matrices A and B (and, in particular, constant matrices), we will see that the Kalman rank condition characterizes the controllability properties of the system. When the matrices A and B are constant and condition rank [A|B] = n holds, we will be able to state a Carleman inequality for the corresponding adjoint problem.
publishDate 2009
dc.date.none.fl_str_mv 2009
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/48942
https://doi.org/10.7153/dea-01-24
url http://hdl.handle.net/11441/48942
https://doi.org/10.7153/dea-01-24
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Differential Equations & Application, 1 (3), 427-457.
ANR-07-JCJC-0139-01
MTM2006-07932
http://files.ele-math.com/articles/dea-01-24.pdf
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Ele-Math
publisher.none.fl_str_mv Ele-Math
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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