Conditions for feedback stabilizability in switched linear systems
Resumen:
This communication is concerned with state- feedback stabilizability of discrete-time switched linear systems. Necessary and sufficient conditions for state-feedback exponential stabilizability are presented. It is shown that, a switched linear system is state-feedback exponentially stabilizable if and only if an associated sequence converges to zero. Equivalently, a switched linear system is state-feedback exponentially stabilizable if and only if a dynamic programming equation admits a solution of some kind. We also address the issue of testing the stabilizability of a given switched system by computing the elements of a new associated sequence of upper bounds for the elements of the previously mentioned sequence. These computations involve the solution of convex programming problems. The elements of both associated sequences are shown to be related via Lagrange duality. Numerical examples illustrate some of the results reported in the paper.
| 2008 | |
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Asymptotic stability Convex programming Discrete time systems Dynamic programming Linear systems |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/38616 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1807522933178892288 |
|---|---|
| author | Najson, Federico |
| author_facet | Najson, Federico |
| author_role | author |
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| collection | COLIBRI |
| dc.creator.none.fl_str_mv | Najson, Federico |
| dc.date.accessioned.none.fl_str_mv | 2023-08-01T20:33:02Z |
| dc.date.available.none.fl_str_mv | 2023-08-01T20:33:02Z |
| dc.date.issued.es.fl_str_mv | 2008 |
| dc.date.submitted.es.fl_str_mv | 20230801 |
| dc.description.abstract.none.fl_txt_mv | This communication is concerned with state- feedback stabilizability of discrete-time switched linear systems. Necessary and sufficient conditions for state-feedback exponential stabilizability are presented. It is shown that, a switched linear system is state-feedback exponentially stabilizable if and only if an associated sequence converges to zero. Equivalently, a switched linear system is state-feedback exponentially stabilizable if and only if a dynamic programming equation admits a solution of some kind. We also address the issue of testing the stabilizability of a given switched system by computing the elements of a new associated sequence of upper bounds for the elements of the previously mentioned sequence. These computations involve the solution of convex programming problems. The elements of both associated sequences are shown to be related via Lagrange duality. Numerical examples illustrate some of the results reported in the paper. |
| dc.identifier.citation.es.fl_str_mv | Najson, Federico. Conditions for feedback stabilizability in switched linear systems. American Control Conference, Seattle, WA, USA, 2008. doi: 10.1109/ACC.2008.4587228 |
| dc.identifier.doi.es.fl_str_mv | doi: 10.1109/ACC.2008.4587228 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/38616 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.publisher.es.fl_str_mv | AACC |
| dc.relation.ispartof.es.fl_str_mv | American Control Conference, Seattle, WA, USA, 2008 |
| dc.rights.license.none.fl_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.source.none.fl_str_mv | reponame:COLIBRI instname:Universidad de la República instacron:Universidad de la República |
| dc.subject.es.fl_str_mv | Asymptotic stability Convex programming Discrete time systems Dynamic programming Linear systems |
| dc.title.none.fl_str_mv | Conditions for feedback stabilizability in switched linear systems |
| dc.type.es.fl_str_mv | Ponencia |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/conferenceObject |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/publishedVersion |
| description | This communication is concerned with state- feedback stabilizability of discrete-time switched linear systems. Necessary and sufficient conditions for state-feedback exponential stabilizability are presented. It is shown that, a switched linear system is state-feedback exponentially stabilizable if and only if an associated sequence converges to zero. Equivalently, a switched linear system is state-feedback exponentially stabilizable if and only if a dynamic programming equation admits a solution of some kind. We also address the issue of testing the stabilizability of a given switched system by computing the elements of a new associated sequence of upper bounds for the elements of the previously mentioned sequence. These computations involve the solution of convex programming problems. The elements of both associated sequences are shown to be related via Lagrange duality. Numerical examples illustrate some of the results reported in the paper. |
| eu_rights_str_mv | openAccess |
| format | conferenceObject |
| id | COLIBRI_fe2b2a1f98ff2c8f67022fcf19195b73 |
| identifier_str_mv | Najson, Federico. Conditions for feedback stabilizability in switched linear systems. American Control Conference, Seattle, WA, USA, 2008. doi: 10.1109/ACC.2008.4587228 doi: 10.1109/ACC.2008.4587228 |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language | eng |
| language_invalid_str_mv | en |
| network_acronym_str | COLIBRI |
| network_name_str | COLIBRI |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/38616 |
| publishDate | 2008 |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | mabel.seroubian@seciu.edu.uy |
| repository.name.fl_str_mv | COLIBRI - Universidad de la República |
| repository_id_str | 4771 |
| rights_invalid_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| spelling | 2023-08-01T20:33:02Z2023-08-01T20:33:02Z200820230801Najson, Federico. Conditions for feedback stabilizability in switched linear systems. American Control Conference, Seattle, WA, USA, 2008. doi: 10.1109/ACC.2008.4587228https://hdl.handle.net/20.500.12008/38616doi: 10.1109/ACC.2008.4587228This communication is concerned with state- feedback stabilizability of discrete-time switched linear systems. Necessary and sufficient conditions for state-feedback exponential stabilizability are presented. It is shown that, a switched linear system is state-feedback exponentially stabilizable if and only if an associated sequence converges to zero. Equivalently, a switched linear system is state-feedback exponentially stabilizable if and only if a dynamic programming equation admits a solution of some kind. We also address the issue of testing the stabilizability of a given switched system by computing the elements of a new associated sequence of upper bounds for the elements of the previously mentioned sequence. These computations involve the solution of convex programming problems. The elements of both associated sequences are shown to be related via Lagrange duality. Numerical examples illustrate some of the results reported in the paper.Made available in DSpace on 2023-08-01T20:33:02Z (GMT). No. of bitstreams: 5 Naj08.pdf: 256881 bytes, checksum: 2b5b0534d71534bd93cc68cfe6a8216a (MD5) license_text: 21936 bytes, checksum: 9833653f73f7853880c94a6fead477b1 (MD5) license_url: 49 bytes, checksum: 4afdbb8c545fd630ea7db775da747b2f (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) license.txt: 4194 bytes, checksum: 7f2e2c17ef6585de66da58d1bfa8b5e1 (MD5) Previous issue date: 2008enengAACCAmerican Control Conference, Seattle, WA, USA, 2008Las 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 - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)Asymptotic stabilityConvex programmingDiscrete time systemsDynamic programmingLinear systemsConditions for feedback stabilizability in switched linear systemsPonenciainfo:eu-repo/semantics/conferenceObjectinfo:eu-repo/semantics/publishedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaNajson, 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- Universidad de la Repúblicafalse |
| spellingShingle | Conditions for feedback stabilizability in switched linear systems Najson, Federico Asymptotic stability Convex programming Discrete time systems Dynamic programming Linear systems |
| status_str | publishedVersion |
| title | Conditions for feedback stabilizability in switched linear systems |
| title_full | Conditions for feedback stabilizability in switched linear systems |
| title_fullStr | Conditions for feedback stabilizability in switched linear systems |
| title_full_unstemmed | Conditions for feedback stabilizability in switched linear systems |
| title_short | Conditions for feedback stabilizability in switched linear systems |
| title_sort | Conditions for feedback stabilizability in switched linear systems |
| topic | Asymptotic stability Convex programming Discrete time systems Dynamic programming Linear systems |
| url | https://hdl.handle.net/20.500.12008/38616 |
