Sufficient conditions for generic feedback stabilizability of switching systems via lie-algebraic solvability

Autores
Haimovich, Hernan; Braslavsky, Julio H.
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We address the stabilization of switching linear systems (SLSs) with control inputs under arbitrary switching. A sufficient condition for the stability of autonomous (without control inputs) SLSs is that the individual subsystems are stable and the Lie algebra generated by their evolution matrices is solvable. This sufficient condition for stability is known to be extremely restrictive and therefore of very limited applicability. Our main contribution is to show that, in contrast to the autonomous case, when control inputs are present the existence of feedback matrices for each subsystem so that the corresponding closed-loop matrices satisfy the aforementioned Lie-algebraic stability condition can become a generic property, hence substantially improving the applicability of such Lie-algebraic techniques in some cases. Since the validity of this Lie-algebraic stability condition implies the existence of a common quadratic Lyapunov function (CQLF) for the SLS, our results yield an analytic sufficient condition for the generic existence of a control CQLF for the SLS.
Fil: Haimovich, Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y Sistemas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura. Escuela de Ingeniería Electrónica. Departamento de Control. Laboratorio de Sistemas Dinámicos y Procesamiento de Información; Argentina
Fil: Braslavsky, Julio H.. Australian Commonwealth Scientific and Industrial Research Organization. Division of Energy Technology; Australia
Materia
Common Quadratic Lyapunov Function
Switching Linear Systems
Uniform Global Exponential Stability
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:11336/3199
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/3199
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Sufficient conditions for generic feedback stabilizability of switching systems via lie-algebraic solvabilityHaimovich, HernanBraslavsky, Julio H.Common Quadratic Lyapunov FunctionSwitching Linear SystemsUniform Global Exponential Stabilityhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1https://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2https://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2We address the stabilization of switching linear systems (SLSs) with control inputs under arbitrary switching. A sufficient condition for the stability of autonomous (without control inputs) SLSs is that the individual subsystems are stable and the Lie algebra generated by their evolution matrices is solvable. This sufficient condition for stability is known to be extremely restrictive and therefore of very limited applicability. Our main contribution is to show that, in contrast to the autonomous case, when control inputs are present the existence of feedback matrices for each subsystem so that the corresponding closed-loop matrices satisfy the aforementioned Lie-algebraic stability condition can become a generic property, hence substantially improving the applicability of such Lie-algebraic techniques in some cases. Since the validity of this Lie-algebraic stability condition implies the existence of a common quadratic Lyapunov function (CQLF) for the SLS, our results yield an analytic sufficient condition for the generic existence of a control CQLF for the SLS.Fil: Haimovich, Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y Sistemas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura. Escuela de Ingeniería Electrónica. Departamento de Control. Laboratorio de Sistemas Dinámicos y Procesamiento de Información; ArgentinaFil: Braslavsky, Julio H.. Australian Commonwealth Scientific and Industrial Research Organization. Division of Energy Technology; AustraliaInstitute of Electrical and Electronics Engineers2013-02-18info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/3199Haimovich, Hernan; Braslavsky, Julio H.; Sufficient conditions for generic feedback stabilizability of switching systems via lie-algebraic solvability; Institute of Electrical and Electronics Engineers; IEEE Transactions on Automatic Control; 58; 3; 18-2-2013; 814-8200018-9286enginfo:eu-repo/semantics/altIdentifier/url/https://ieeexplore.ieee.org/document/6298939info:eu-repo/semantics/altIdentifier/doi/10.1109/TAC.2012.2218151info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:03:44Zoai:ri.conicet.gov.ar:11336/3199instacron: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:34982025-09-29 10:03:44.548CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Sufficient conditions for generic feedback stabilizability of switching systems via lie-algebraic solvability
title Sufficient conditions for generic feedback stabilizability of switching systems via lie-algebraic solvability
spellingShingle Sufficient conditions for generic feedback stabilizability of switching systems via lie-algebraic solvability
Haimovich, Hernan
Common Quadratic Lyapunov Function
Switching Linear Systems
Uniform Global Exponential Stability
title_short Sufficient conditions for generic feedback stabilizability of switching systems via lie-algebraic solvability
title_full Sufficient conditions for generic feedback stabilizability of switching systems via lie-algebraic solvability
title_fullStr Sufficient conditions for generic feedback stabilizability of switching systems via lie-algebraic solvability
title_full_unstemmed Sufficient conditions for generic feedback stabilizability of switching systems via lie-algebraic solvability
title_sort Sufficient conditions for generic feedback stabilizability of switching systems via lie-algebraic solvability
dc.creator.none.fl_str_mv Haimovich, Hernan
Braslavsky, Julio H.
author Haimovich, Hernan
author_facet Haimovich, Hernan
Braslavsky, Julio H.
author_role author
author2 Braslavsky, Julio H.
author2_role author
dc.subject.none.fl_str_mv Common Quadratic Lyapunov Function
Switching Linear Systems
Uniform Global Exponential Stability
topic Common Quadratic Lyapunov Function
Switching Linear Systems
Uniform Global Exponential Stability
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/2.2
https://purl.org/becyt/ford/2
https://purl.org/becyt/ford/2.2
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv We address the stabilization of switching linear systems (SLSs) with control inputs under arbitrary switching. A sufficient condition for the stability of autonomous (without control inputs) SLSs is that the individual subsystems are stable and the Lie algebra generated by their evolution matrices is solvable. This sufficient condition for stability is known to be extremely restrictive and therefore of very limited applicability. Our main contribution is to show that, in contrast to the autonomous case, when control inputs are present the existence of feedback matrices for each subsystem so that the corresponding closed-loop matrices satisfy the aforementioned Lie-algebraic stability condition can become a generic property, hence substantially improving the applicability of such Lie-algebraic techniques in some cases. Since the validity of this Lie-algebraic stability condition implies the existence of a common quadratic Lyapunov function (CQLF) for the SLS, our results yield an analytic sufficient condition for the generic existence of a control CQLF for the SLS.
Fil: Haimovich, Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y Sistemas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura. Escuela de Ingeniería Electrónica. Departamento de Control. Laboratorio de Sistemas Dinámicos y Procesamiento de Información; Argentina
Fil: Braslavsky, Julio H.. Australian Commonwealth Scientific and Industrial Research Organization. Division of Energy Technology; Australia
description We address the stabilization of switching linear systems (SLSs) with control inputs under arbitrary switching. A sufficient condition for the stability of autonomous (without control inputs) SLSs is that the individual subsystems are stable and the Lie algebra generated by their evolution matrices is solvable. This sufficient condition for stability is known to be extremely restrictive and therefore of very limited applicability. Our main contribution is to show that, in contrast to the autonomous case, when control inputs are present the existence of feedback matrices for each subsystem so that the corresponding closed-loop matrices satisfy the aforementioned Lie-algebraic stability condition can become a generic property, hence substantially improving the applicability of such Lie-algebraic techniques in some cases. Since the validity of this Lie-algebraic stability condition implies the existence of a common quadratic Lyapunov function (CQLF) for the SLS, our results yield an analytic sufficient condition for the generic existence of a control CQLF for the SLS.
publishDate 2013
dc.date.none.fl_str_mv 2013-02-18
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/11336/3199
Haimovich, Hernan; Braslavsky, Julio H.; Sufficient conditions for generic feedback stabilizability of switching systems via lie-algebraic solvability; Institute of Electrical and Electronics Engineers; IEEE Transactions on Automatic Control; 58; 3; 18-2-2013; 814-820
0018-9286
url http://hdl.handle.net/11336/3199
identifier_str_mv Haimovich, Hernan; Braslavsky, Julio H.; Sufficient conditions for generic feedback stabilizability of switching systems via lie-algebraic solvability; Institute of Electrical and Electronics Engineers; IEEE Transactions on Automatic Control; 58; 3; 18-2-2013; 814-820
0018-9286
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://ieeexplore.ieee.org/document/6298939
info:eu-repo/semantics/altIdentifier/doi/10.1109/TAC.2012.2218151
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 Institute of Electrical and Electronics Engineers
publisher.none.fl_str_mv Institute of Electrical and Electronics Engineers
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 13.070432

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