Controllability and feedback stabilizability in a nonuniform framework.
We propose a new controllability property for linear nonautonomous control systems in finite dimension: the nonuniform complete controllability, which is halfway between the classical Kalman’s properties of complete controllability and uniform complete controllability. This new concept has a strong...
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| Format: | article |
| Language: | English French |
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2024
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.672/ https://hdl.handle.net/20.500.12008/48559 |
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| _version_ | 1868890241974140928 |
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| author | Huerta, Ignacio |
| author2 | Monzón, Pablo Robledo, Gonzalo |
| author2_role | author author |
| author_browse | Huerta, Ignacio Monzón, Pablo Robledo, Gonzalo |
| author_facet | Huerta, Ignacio Monzón, Pablo Robledo, Gonzalo |
| author_role | author |
| collection | COLIBRI |
| dc.contributor.none.fl_str_mv | Huerta Ignacio, Universidad Técnica Federico Santa María, Valparaíso, Chile Monzón Pablo, Universidad de la República (Uruguay). Facultad de Ingeniería. Robledo Gonzalo, Universidad de Chile, Santiago, Chile |
| dc.creator.none.fl_str_mv | Huerta, Ignacio Monzón, Pablo Robledo, Gonzalo |
| dc.date.none.fl_str_mv | 2024 2025-02-28T17:41:54Z 2025-02-28T17:41:54Z |
| dc.format.none.fl_str_mv | 27 p. application/pdf |
| dc.identifier.none.fl_str_mv | Huerta, I., Monzón, P. y Robledo, G. "Controllability and feedback stabilizability in a nonuniform framework". Comptes Rendus. Mathématique. [en línea]. 2024, vol. 362, pp. 1667-1692. DOI: 10.5802/crmath.672. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.672/ https://hdl.handle.net/20.500.12008/48559 10.5802/crmath.672 1778-3569 |
| dc.language.none.fl_str_mv | en fr eng fra |
| dc.publisher.none.fl_str_mv | Centre Mersenne |
| dc.relation.none.fl_str_mv | Comptes Rendus. Mathématique, vol. 362, 2024, pp. 1667-1692. |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess Licencia Creative Commons Atribución (CC - By 4.0) |
| dc.source.none.fl_str_mv | reponame:COLIBRI instname:Universidad de la República instacron:Universidad de la República |
| dc.subject.none.fl_str_mv | Linear nonautonomous systems Nonuniform controllability Nonuniform exponential stabilizability Nonuniform bounded growth Systèmes linéaires non autonomes Contrôlabilité non uniforme Stabilité exponentielle non uniforme Croissance bornée non uniforme |
| dc.title.none.fl_str_mv | Controllability and feedback stabilizability in a nonuniform framework. |
| dc.type.none.fl_str_mv | Artículo info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
| description | We propose a new controllability property for linear nonautonomous control systems in finite dimension: the nonuniform complete controllability, which is halfway between the classical Kalman’s properties of complete controllability and uniform complete controllability. This new concept has a strong linkage, as we prove, with the property of nonuniform bounded growth for the corresponding plant. In addition, we also prove that if a control system is nonuniformly completely controllable and its plant (uncontrolled part) has the property of nonuniform bounded growth, then there exist a linear feedback control leading to a nonuniformly exponentially stable closed–loop system. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | anni_f9ad91ed8fc1d7ee56864bf4e00ca487 |
| identifier_str_mv | Huerta, I., Monzón, P. y Robledo, G. "Controllability and feedback stabilizability in a nonuniform framework". Comptes Rendus. Mathématique. [en línea]. 2024, vol. 362, pp. 1667-1692. DOI: 10.5802/crmath.672. 10.5802/crmath.672 1778-3569 |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language | eng fra |
| language_invalid_str_mv | en fr |
| network_acronym_str | anni |
| network_name_str | oai-lr-anni |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/48559 |
| publishDate | 2024 |
| publishDateSort | 2024 |
| publisher.none.fl_str_mv | Centre Mersenne |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | Licencia Creative Commons Atribución (CC - By 4.0) |
| spelling | Controllability and feedback stabilizability in a nonuniform framework.Huerta, IgnacioMonzón, PabloRobledo, GonzaloLinear nonautonomous systemsNonuniform controllabilityNonuniform exponential stabilizabilityNonuniform bounded growthSystèmes linéaires non autonomesContrôlabilité non uniformeStabilité exponentielle non uniformeCroissance bornée non uniformeWe propose a new controllability property for linear nonautonomous control systems in finite dimension: the nonuniform complete controllability, which is halfway between the classical Kalman’s properties of complete controllability and uniform complete controllability. This new concept has a strong linkage, as we prove, with the property of nonuniform bounded growth for the corresponding plant. In addition, we also prove that if a control system is nonuniformly completely controllable and its plant (uncontrolled part) has the property of nonuniform bounded growth, then there exist a linear feedback control leading to a nonuniformly exponentially stable closed–loop system.Nous proposons une nouvelle propriété de contrôlabilité pour des systèmes de contrôle linéaires non autonomes en dimension finie: la contrôlabilité complète non uniforme, qui est à mi-chemin entre les propriétés classiques de contrôlabilité complète et la contrôlabilité complète uniforme établies par Kalman. Ce nouveau concept à un lien étroit, comme nous le prouvons, avec la propriété de croissance bornée non uniforme de la plante correspondante. En outre, il est aussi prouvé que si un système de contrôle est non uniformément complètement contrôlable et sa plante (partie non contrôlée) à la propriété de croissance bornée non uniforme, alors on a un résultat de stabilisation asymptotique par bouclage linéaire ou la convergence est non uniformément exponentielle.Esta investigación ha sido financiada por las becas FONDECYT Regular 1210733 y FONDECYT Postdoctorado 3210132.Centre MersenneHuerta Ignacio, Universidad Técnica Federico Santa María, Valparaíso, ChileMonzón Pablo, Universidad de la República (Uruguay). Facultad de Ingeniería.Robledo Gonzalo, Universidad de Chile, Santiago, Chile2025-02-28T17:41:54Z2025-02-28T17:41:54Z2024Artículoinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion27 p.application/pdfHuerta, I., Monzón, P. y Robledo, G. "Controllability and feedback stabilizability in a nonuniform framework". Comptes Rendus. Mathématique. [en línea]. 2024, vol. 362, pp. 1667-1692. DOI: 10.5802/crmath.672.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.672/https://hdl.handle.net/20.500.12008/4855910.5802/crmath.6721778-3569reponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaenfrengfraComptes Rendus. Mathématique, vol. 362, 2024, pp. 1667-1692.Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad de la República.(Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución (CC - By 4.0)oai:colibri.udelar.edu.uy:20.500.12008/485592026-04-14T10:16:04Z |
| spellingShingle | Controllability and feedback stabilizability in a nonuniform framework. Huerta, Ignacio Linear nonautonomous systems Nonuniform controllability Nonuniform exponential stabilizability Nonuniform bounded growth Systèmes linéaires non autonomes Contrôlabilité non uniforme Stabilité exponentielle non uniforme Croissance bornée non uniforme |
| status_str | publishedVersion |
| title | Controllability and feedback stabilizability in a nonuniform framework. |
| title_full | Controllability and feedback stabilizability in a nonuniform framework. |
| title_fullStr | Controllability and feedback stabilizability in a nonuniform framework. |
| title_full_unstemmed | Controllability and feedback stabilizability in a nonuniform framework. |
| title_short | Controllability and feedback stabilizability in a nonuniform framework. |
| title_sort | Controllability and feedback stabilizability in a nonuniform framework. |
| topic | Linear nonautonomous systems Nonuniform controllability Nonuniform exponential stabilizability Nonuniform bounded growth Systèmes linéaires non autonomes Contrôlabilité non uniforme Stabilité exponentielle non uniforme Croissance bornée non uniforme |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.672/ https://hdl.handle.net/20.500.12008/48559 |