Componentwise ultimate bound and invariant set computation for switched linear systems

Autores
Haimovich, Hernan; Seron, Maria Marta
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We present a novel ultimate bound and invariant set computation method for continuous-time switched linear systems with disturbances and arbitrary switching. The proposed method relies on the existence of a transformation that takes all matrices of the switched linear system into a convenient form satisfying certain properties. The method provides ultimate bounds and invariant sets in the form of polyhedral and/or mixed ellipsoidal/polyhedral sets, is completely systematic once the aforementioned transformation is obtained, and provides a new sufficient condition for practical stability. We show that the transformation required by our method can easily be found in the well-known case where the subsystem matrices generate a solvable Lie algebra, and we provide an algorithm to seek such transformation in the general case. An example comparing the bounds obtained by the proposed method with those obtained from a common quadratic Lyapunov function computed via linear matrix inequalities shows a clear advantage of the proposed method in some cases.
Fil: Haimovich, Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura. Escuela de Ingeniería Electrónica. Departamento de Control; Argentina
Fil: Seron, Maria Marta. Universidad de Newcastle Australia. Centro de Excelencia en Sistemas Dinámicos Complejos y Control; Australia
Materia
Ultimate bounds
Invariant sets
Switched systems
Componentwise methods
Solvable Lie algebras
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/280913
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/280913
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Componentwise ultimate bound and invariant set computation for switched linear systemsHaimovich, HernanSeron, Maria MartaUltimate boundsInvariant setsSwitched systemsComponentwise methodsSolvable Lie algebrashttps://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2We present a novel ultimate bound and invariant set computation method for continuous-time switched linear systems with disturbances and arbitrary switching. The proposed method relies on the existence of a transformation that takes all matrices of the switched linear system into a convenient form satisfying certain properties. The method provides ultimate bounds and invariant sets in the form of polyhedral and/or mixed ellipsoidal/polyhedral sets, is completely systematic once the aforementioned transformation is obtained, and provides a new sufficient condition for practical stability. We show that the transformation required by our method can easily be found in the well-known case where the subsystem matrices generate a solvable Lie algebra, and we provide an algorithm to seek such transformation in the general case. An example comparing the bounds obtained by the proposed method with those obtained from a common quadratic Lyapunov function computed via linear matrix inequalities shows a clear advantage of the proposed method in some cases.Fil: Haimovich, Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura. Escuela de Ingeniería Electrónica. Departamento de Control; ArgentinaFil: Seron, Maria Marta. Universidad de Newcastle Australia. Centro de Excelencia en Sistemas Dinámicos Complejos y Control; AustraliaPergamon-Elsevier Science Ltd2010-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/280913Haimovich, Hernan; Seron, Maria Marta; Componentwise ultimate bound and invariant set computation for switched linear systems; Pergamon-Elsevier Science Ltd; Automatica; 46; 11; 11-2010; 1897-19010005-1098CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0005109810003687info:eu-repo/semantics/altIdentifier/doi/10.1016/j.automatica.2010.08.018info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2026-02-26T09:57:20Zoai:ri.conicet.gov.ar:11336/280913instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982026-02-26 09:57:20.475CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Componentwise ultimate bound and invariant set computation for switched linear systems
title Componentwise ultimate bound and invariant set computation for switched linear systems
spellingShingle Componentwise ultimate bound and invariant set computation for switched linear systems
Haimovich, Hernan
Ultimate bounds
Invariant sets
Switched systems
Componentwise methods
Solvable Lie algebras
title_short Componentwise ultimate bound and invariant set computation for switched linear systems
title_full Componentwise ultimate bound and invariant set computation for switched linear systems
title_fullStr Componentwise ultimate bound and invariant set computation for switched linear systems
title_full_unstemmed Componentwise ultimate bound and invariant set computation for switched linear systems
title_sort Componentwise ultimate bound and invariant set computation for switched linear systems
dc.creator.none.fl_str_mv Haimovich, Hernan
Seron, Maria Marta
author Haimovich, Hernan
author_facet Haimovich, Hernan
Seron, Maria Marta
author_role author
author2 Seron, Maria Marta
author2_role author
dc.subject.none.fl_str_mv Ultimate bounds
Invariant sets
Switched systems
Componentwise methods
Solvable Lie algebras
topic Ultimate bounds
Invariant sets
Switched systems
Componentwise methods
Solvable Lie algebras
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.2
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv We present a novel ultimate bound and invariant set computation method for continuous-time switched linear systems with disturbances and arbitrary switching. The proposed method relies on the existence of a transformation that takes all matrices of the switched linear system into a convenient form satisfying certain properties. The method provides ultimate bounds and invariant sets in the form of polyhedral and/or mixed ellipsoidal/polyhedral sets, is completely systematic once the aforementioned transformation is obtained, and provides a new sufficient condition for practical stability. We show that the transformation required by our method can easily be found in the well-known case where the subsystem matrices generate a solvable Lie algebra, and we provide an algorithm to seek such transformation in the general case. An example comparing the bounds obtained by the proposed method with those obtained from a common quadratic Lyapunov function computed via linear matrix inequalities shows a clear advantage of the proposed method in some cases.
Fil: Haimovich, Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura. Escuela de Ingeniería Electrónica. Departamento de Control; Argentina
Fil: Seron, Maria Marta. Universidad de Newcastle Australia. Centro de Excelencia en Sistemas Dinámicos Complejos y Control; Australia
description We present a novel ultimate bound and invariant set computation method for continuous-time switched linear systems with disturbances and arbitrary switching. The proposed method relies on the existence of a transformation that takes all matrices of the switched linear system into a convenient form satisfying certain properties. The method provides ultimate bounds and invariant sets in the form of polyhedral and/or mixed ellipsoidal/polyhedral sets, is completely systematic once the aforementioned transformation is obtained, and provides a new sufficient condition for practical stability. We show that the transformation required by our method can easily be found in the well-known case where the subsystem matrices generate a solvable Lie algebra, and we provide an algorithm to seek such transformation in the general case. An example comparing the bounds obtained by the proposed method with those obtained from a common quadratic Lyapunov function computed via linear matrix inequalities shows a clear advantage of the proposed method in some cases.
publishDate 2010
dc.date.none.fl_str_mv 2010-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/280913
Haimovich, Hernan; Seron, Maria Marta; Componentwise ultimate bound and invariant set computation for switched linear systems; Pergamon-Elsevier Science Ltd; Automatica; 46; 11; 11-2010; 1897-1901
0005-1098
CONICET Digital
CONICET
url http://hdl.handle.net/11336/280913
identifier_str_mv Haimovich, Hernan; Seron, Maria Marta; Componentwise ultimate bound and invariant set computation for switched linear systems; Pergamon-Elsevier Science Ltd; Automatica; 46; 11; 11-2010; 1897-1901
0005-1098
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0005109810003687
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.automatica.2010.08.018
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Pergamon-Elsevier Science Ltd
publisher.none.fl_str_mv Pergamon-Elsevier Science Ltd
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.176822

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