On the regulator problem for linear systems over rings and algebras

[EN] The regulator problem is solvable for a linear dynamical system Σ if and only if Σ is both pole assignable and state estimable. In this case, Σ is a canonical system (i.e., reachable and observable). When the ring R is a field or a Noetherian total ring of fractions the converse is true. Commut...

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Autores: Hermida Alonso, José Ángel, Carriegos Vieira, Miguel, Sáez Schwedt, Andrés, Sánchez Giralda, Tomás
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2021
País:España
Institución:Universidad Rey Juan Carlos
Repositorio:BULERIA. Repositorio Institucional de la Universidad de León
OAI Identifier:oai:buleria.unileon.es:10612/19427
Acceso en línea:https://www.degruyter.com/document/doi/10.1515/math-2021-0002/html
https://hdl.handle.net/10612/19427
Access Level:acceso abierto
Palabra clave:Matemáticas
Linear systems over commutative rings
Regulator problem
Duality principle
Pole assignment
1201.05 Campos, Anillos, Álgebras
1201.10 Álgebra Lineal
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oai_identifier_str oai:buleria.unileon.es:10612/19427
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repository_id_str
spelling On the regulator problem for linear systems over rings and algebrasHermida Alonso, José ÁngelCarriegos Vieira, MiguelSáez Schwedt, AndrésSánchez Giralda, TomásMatemáticasLinear systems over commutative ringsRegulator problemDuality principlePole assignment1201.05 Campos, Anillos, Álgebras1201.10 Álgebra Lineal[EN] The regulator problem is solvable for a linear dynamical system Σ if and only if Σ is both pole assignable and state estimable. In this case, Σ is a canonical system (i.e., reachable and observable). When the ring R is a field or a Noetherian total ring of fractions the converse is true. Commutative rings which have the property that the regulator problem is solvable for every canonical system (RP-rings) are characterized as the class of rings where every observable system is state estimable (SE-rings), and this class is shown to be equal to the class of rings where every reachable system is pole-assignable (PA-rings) and the dual of a canonical system is also canonical (DP-rings).SIThis research was partially supported by RIASC, Research Institute of Applied Sciences and Cybersecurity (riasc.unileon.es).De GruyterMatematica AplicadaEscuela de Ingenierias Industrial, Informática y Aeroespacial2021info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttps://www.degruyter.com/document/doi/10.1515/math-2021-0002/htmlhttps://hdl.handle.net/10612/19427reponame:BULERIA. Repositorio Institucional de la Universidad de Leóninstname:Universidad Rey Juan CarlosIngléshttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:buleria.unileon.es:10612/194272026-06-24T12:43:27Z
dc.title.none.fl_str_mv On the regulator problem for linear systems over rings and algebras
title On the regulator problem for linear systems over rings and algebras
spellingShingle On the regulator problem for linear systems over rings and algebras
Hermida Alonso, José Ángel
Matemáticas
Linear systems over commutative rings
Regulator problem
Duality principle
Pole assignment
1201.05 Campos, Anillos, Álgebras
1201.10 Álgebra Lineal
title_short On the regulator problem for linear systems over rings and algebras
title_full On the regulator problem for linear systems over rings and algebras
title_fullStr On the regulator problem for linear systems over rings and algebras
title_full_unstemmed On the regulator problem for linear systems over rings and algebras
title_sort On the regulator problem for linear systems over rings and algebras
dc.creator.none.fl_str_mv Hermida Alonso, José Ángel
Carriegos Vieira, Miguel
Sáez Schwedt, Andrés
Sánchez Giralda, Tomás
author Hermida Alonso, José Ángel
author_facet Hermida Alonso, José Ángel
Carriegos Vieira, Miguel
Sáez Schwedt, Andrés
Sánchez Giralda, Tomás
author_role author
author2 Carriegos Vieira, Miguel
Sáez Schwedt, Andrés
Sánchez Giralda, Tomás
author2_role author
author
author
dc.contributor.none.fl_str_mv Matematica Aplicada
Escuela de Ingenierias Industrial, Informática y Aeroespacial
dc.subject.none.fl_str_mv Matemáticas
Linear systems over commutative rings
Regulator problem
Duality principle
Pole assignment
1201.05 Campos, Anillos, Álgebras
1201.10 Álgebra Lineal
topic Matemáticas
Linear systems over commutative rings
Regulator problem
Duality principle
Pole assignment
1201.05 Campos, Anillos, Álgebras
1201.10 Álgebra Lineal
description [EN] The regulator problem is solvable for a linear dynamical system Σ if and only if Σ is both pole assignable and state estimable. In this case, Σ is a canonical system (i.e., reachable and observable). When the ring R is a field or a Noetherian total ring of fractions the converse is true. Commutative rings which have the property that the regulator problem is solvable for every canonical system (RP-rings) are characterized as the class of rings where every observable system is state estimable (SE-rings), and this class is shown to be equal to the class of rings where every reachable system is pole-assignable (PA-rings) and the dual of a canonical system is also canonical (DP-rings).
publishDate 2021
dc.date.none.fl_str_mv 2021
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 https://www.degruyter.com/document/doi/10.1515/math-2021-0002/html
https://hdl.handle.net/10612/19427
url https://www.degruyter.com/document/doi/10.1515/math-2021-0002/html
https://hdl.handle.net/10612/19427
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv http://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv De Gruyter
publisher.none.fl_str_mv De Gruyter
dc.source.none.fl_str_mv reponame:BULERIA. Repositorio Institucional de la Universidad de León
instname:Universidad Rey Juan Carlos
instname_str Universidad Rey Juan Carlos
reponame_str BULERIA. Repositorio Institucional de la Universidad de León
collection BULERIA. Repositorio Institucional de la Universidad de León
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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