Global Stability Results for Switched Systems Based on Weak Lyapunov Functions

Autores
Mancilla Aguilar, Jose Luis; Haimovich, Hernan; Garcia Galiñanes, Rafael Antonio
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we study the stability of nonlinear and time-varying switched systems under restricted switching. We approach the problem by decomposing the system dynamics into a nominal-like part and a perturbation-like one. Most stability results for perturbed systems are based on the use of strong Lyapunov functions, i.e. functions of time and state whose total time derivative along the nominal system trajectories is bounded by a negative definite function of the state. However, switched systems under restricted switching may not admit strong Lyapunov functions, even when asymptotic stability is uniform over the set of switching signals considered. The main contribution of the current paper consists in providing stability results that are based on the stability of the nominal-like part of the system and require only a weak Lyapunov function. These results may have wider applicability than results based on strong Lyapunov functions. The results provided follow two lines. First, we give very general global uniform asymptotic stability results under reasonable boundedness conditions on the functions that define the dynamics of the nominal-like and the perturbation-like parts of the system. Second, we provide input-to-state stability (ISS) results for the case when the nominal-like part is switched linear-time-varying. We provide two types of ISS results: Standard ISS that involves the essential supremum norm of the input and a modified ISS that involves a power-type norm.
Fil: Mancilla Aguilar, Jose Luis. Instituto Tecnológico de Buenos Aires; Argentina
Fil: Haimovich, Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; Argentina
Fil: Garcia Galiñanes, Rafael Antonio. Instituto Tecnológico de Buenos Aires; Argentina
Materia
Asymptotic Stability
Input-To-State Stability
Lyapunov Methods
Nonlinear Dynamical Systems
Switched Systems
Time-Varying Systems
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:11336/53282
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/53282
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Global Stability Results for Switched Systems Based on Weak Lyapunov FunctionsMancilla Aguilar, Jose LuisHaimovich, HernanGarcia Galiñanes, Rafael AntonioAsymptotic StabilityInput-To-State StabilityLyapunov MethodsNonlinear Dynamical SystemsSwitched SystemsTime-Varying Systemshttps://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2In this paper we study the stability of nonlinear and time-varying switched systems under restricted switching. We approach the problem by decomposing the system dynamics into a nominal-like part and a perturbation-like one. Most stability results for perturbed systems are based on the use of strong Lyapunov functions, i.e. functions of time and state whose total time derivative along the nominal system trajectories is bounded by a negative definite function of the state. However, switched systems under restricted switching may not admit strong Lyapunov functions, even when asymptotic stability is uniform over the set of switching signals considered. The main contribution of the current paper consists in providing stability results that are based on the stability of the nominal-like part of the system and require only a weak Lyapunov function. These results may have wider applicability than results based on strong Lyapunov functions. The results provided follow two lines. First, we give very general global uniform asymptotic stability results under reasonable boundedness conditions on the functions that define the dynamics of the nominal-like and the perturbation-like parts of the system. Second, we provide input-to-state stability (ISS) results for the case when the nominal-like part is switched linear-time-varying. We provide two types of ISS results: Standard ISS that involves the essential supremum norm of the input and a modified ISS that involves a power-type norm.Fil: Mancilla Aguilar, Jose Luis. Instituto Tecnológico de Buenos Aires; ArgentinaFil: Haimovich, Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; ArgentinaFil: Garcia Galiñanes, Rafael Antonio. Instituto Tecnológico de Buenos Aires; ArgentinaInstitute of Electrical and Electronics Engineers2017-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/53282Mancilla Aguilar, Jose Luis; Haimovich, Hernan; Garcia Galiñanes, Rafael Antonio; Global Stability Results for Switched Systems Based on Weak Lyapunov Functions; Institute of Electrical and Electronics Engineers; IEEE Transactions on Automatic Control; 62; 6; 6-2017; 2764-27770018-9286CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1109/TAC.2016.2627622info:eu-repo/semantics/altIdentifier/url/https://ieeexplore.ieee.org/document/7740968/info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:39:51Zoai:ri.conicet.gov.ar:11336/53282instacron: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:34982025-10-22 11:39:51.686CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Global Stability Results for Switched Systems Based on Weak Lyapunov Functions
title Global Stability Results for Switched Systems Based on Weak Lyapunov Functions
spellingShingle Global Stability Results for Switched Systems Based on Weak Lyapunov Functions
Mancilla Aguilar, Jose Luis
Asymptotic Stability
Input-To-State Stability
Lyapunov Methods
Nonlinear Dynamical Systems
Switched Systems
Time-Varying Systems
title_short Global Stability Results for Switched Systems Based on Weak Lyapunov Functions
title_full Global Stability Results for Switched Systems Based on Weak Lyapunov Functions
title_fullStr Global Stability Results for Switched Systems Based on Weak Lyapunov Functions
title_full_unstemmed Global Stability Results for Switched Systems Based on Weak Lyapunov Functions
title_sort Global Stability Results for Switched Systems Based on Weak Lyapunov Functions
dc.creator.none.fl_str_mv Mancilla Aguilar, Jose Luis
Haimovich, Hernan
Garcia Galiñanes, Rafael Antonio
author Mancilla Aguilar, Jose Luis
author_facet Mancilla Aguilar, Jose Luis
Haimovich, Hernan
Garcia Galiñanes, Rafael Antonio
author_role author
author2 Haimovich, Hernan
Garcia Galiñanes, Rafael Antonio
author2_role author
author
dc.subject.none.fl_str_mv Asymptotic Stability
Input-To-State Stability
Lyapunov Methods
Nonlinear Dynamical Systems
Switched Systems
Time-Varying Systems
topic Asymptotic Stability
Input-To-State Stability
Lyapunov Methods
Nonlinear Dynamical Systems
Switched Systems
Time-Varying Systems
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.2
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv In this paper we study the stability of nonlinear and time-varying switched systems under restricted switching. We approach the problem by decomposing the system dynamics into a nominal-like part and a perturbation-like one. Most stability results for perturbed systems are based on the use of strong Lyapunov functions, i.e. functions of time and state whose total time derivative along the nominal system trajectories is bounded by a negative definite function of the state. However, switched systems under restricted switching may not admit strong Lyapunov functions, even when asymptotic stability is uniform over the set of switching signals considered. The main contribution of the current paper consists in providing stability results that are based on the stability of the nominal-like part of the system and require only a weak Lyapunov function. These results may have wider applicability than results based on strong Lyapunov functions. The results provided follow two lines. First, we give very general global uniform asymptotic stability results under reasonable boundedness conditions on the functions that define the dynamics of the nominal-like and the perturbation-like parts of the system. Second, we provide input-to-state stability (ISS) results for the case when the nominal-like part is switched linear-time-varying. We provide two types of ISS results: Standard ISS that involves the essential supremum norm of the input and a modified ISS that involves a power-type norm.
Fil: Mancilla Aguilar, Jose Luis. Instituto Tecnológico de Buenos Aires; Argentina
Fil: Haimovich, Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; Argentina
Fil: Garcia Galiñanes, Rafael Antonio. Instituto Tecnológico de Buenos Aires; Argentina
description In this paper we study the stability of nonlinear and time-varying switched systems under restricted switching. We approach the problem by decomposing the system dynamics into a nominal-like part and a perturbation-like one. Most stability results for perturbed systems are based on the use of strong Lyapunov functions, i.e. functions of time and state whose total time derivative along the nominal system trajectories is bounded by a negative definite function of the state. However, switched systems under restricted switching may not admit strong Lyapunov functions, even when asymptotic stability is uniform over the set of switching signals considered. The main contribution of the current paper consists in providing stability results that are based on the stability of the nominal-like part of the system and require only a weak Lyapunov function. These results may have wider applicability than results based on strong Lyapunov functions. The results provided follow two lines. First, we give very general global uniform asymptotic stability results under reasonable boundedness conditions on the functions that define the dynamics of the nominal-like and the perturbation-like parts of the system. Second, we provide input-to-state stability (ISS) results for the case when the nominal-like part is switched linear-time-varying. We provide two types of ISS results: Standard ISS that involves the essential supremum norm of the input and a modified ISS that involves a power-type norm.
publishDate 2017
dc.date.none.fl_str_mv 2017-06
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/11336/53282
Mancilla Aguilar, Jose Luis; Haimovich, Hernan; Garcia Galiñanes, Rafael Antonio; Global Stability Results for Switched Systems Based on Weak Lyapunov Functions; Institute of Electrical and Electronics Engineers; IEEE Transactions on Automatic Control; 62; 6; 6-2017; 2764-2777
0018-9286
CONICET Digital
CONICET
url http://hdl.handle.net/11336/53282
identifier_str_mv Mancilla Aguilar, Jose Luis; Haimovich, Hernan; Garcia Galiñanes, Rafael Antonio; Global Stability Results for Switched Systems Based on Weak Lyapunov Functions; Institute of Electrical and Electronics Engineers; IEEE Transactions on Automatic Control; 62; 6; 6-2017; 2764-2777
0018-9286
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1109/TAC.2016.2627622
info:eu-repo/semantics/altIdentifier/url/https://ieeexplore.ieee.org/document/7740968/
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 12.982451

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