Characterization of semiglobal stability properties for discrete-time models of non-uniformly sampled nonlinear systems

Autores
Vallarella, Alexis Javier; Haimovich, Hernan
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Discrete-time models of non-uniformly sampled nonlinear systems under zero-order hold relate the next state sample to the current state sample, (constant) input value, and sampling interval. The exact discrete-time model, that is, the discrete-time model whose state matches that of the continuous-time nonlinear system at the sampling instants may be difficult or even impossible to obtain. In this context, one approach to the analysis of stability is based on the use of an approximate discrete-time model and a bound on the mismatch between the exact and approximate models. This approach requires three conceptually different tasks: (i) ensure the stability of the (approximate) discrete-time model, (ii) ensure that the stability of the approximate model carries over to the exact model, (iii) if necessary, bound intersample behaviour. Existing conditions for ensuring the stability of a discrete-time model as per task (i) have some or all of the following drawbacks: are only sufficient but not necessary; do not allow for varying sampling rate; cannot be applied in the presence of state-measurement or actuation errors. In this paper, we overcome these drawbacks by providing characterizations of, i.e. necessary and sufficient conditions for, two stability properties: semiglobal asymptotic stability, robustly with respect to bounded disturbances, and semiglobal input-to-state stability, where the (disturbance) input may successfully represent state-measurement or actuation errors. Our results can be applied when sampling is not necessarily uniform.
Fil: Vallarella, Alexis Javier. 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: 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
Materia
DISCRETE-TIME MODELS
INPUT-TO-STATE STABILITY (ISS)
NON-UNIFORM SAMPLING
NONLINEAR SYSTEMS
SAMPLED-DATA
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/87977
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Characterization of semiglobal stability properties for discrete-time models of non-uniformly sampled nonlinear systemsVallarella, Alexis JavierHaimovich, HernanDISCRETE-TIME MODELSINPUT-TO-STATE STABILITY (ISS)NON-UNIFORM SAMPLINGNONLINEAR SYSTEMSSAMPLED-DATAhttps://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2https://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Discrete-time models of non-uniformly sampled nonlinear systems under zero-order hold relate the next state sample to the current state sample, (constant) input value, and sampling interval. The exact discrete-time model, that is, the discrete-time model whose state matches that of the continuous-time nonlinear system at the sampling instants may be difficult or even impossible to obtain. In this context, one approach to the analysis of stability is based on the use of an approximate discrete-time model and a bound on the mismatch between the exact and approximate models. This approach requires three conceptually different tasks: (i) ensure the stability of the (approximate) discrete-time model, (ii) ensure that the stability of the approximate model carries over to the exact model, (iii) if necessary, bound intersample behaviour. Existing conditions for ensuring the stability of a discrete-time model as per task (i) have some or all of the following drawbacks: are only sufficient but not necessary; do not allow for varying sampling rate; cannot be applied in the presence of state-measurement or actuation errors. In this paper, we overcome these drawbacks by providing characterizations of, i.e. necessary and sufficient conditions for, two stability properties: semiglobal asymptotic stability, robustly with respect to bounded disturbances, and semiglobal input-to-state stability, where the (disturbance) input may successfully represent state-measurement or actuation errors. Our results can be applied when sampling is not necessarily uniform.Fil: Vallarella, Alexis Javier. 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: 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; ArgentinaElsevier Science2018-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/87977Vallarella, Alexis Javier; Haimovich, Hernan; Characterization of semiglobal stability properties for discrete-time models of non-uniformly sampled nonlinear systems; Elsevier Science; Systems And Control Letters; 122; 12-2018; 60-660167-6911CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.sysconle.2018.10.005info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0167691118301798info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:42:27Zoai:ri.conicet.gov.ar:11336/87977instacron: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 09:42:27.884CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Characterization of semiglobal stability properties for discrete-time models of non-uniformly sampled nonlinear systems
title Characterization of semiglobal stability properties for discrete-time models of non-uniformly sampled nonlinear systems
spellingShingle Characterization of semiglobal stability properties for discrete-time models of non-uniformly sampled nonlinear systems
Vallarella, Alexis Javier
DISCRETE-TIME MODELS
INPUT-TO-STATE STABILITY (ISS)
NON-UNIFORM SAMPLING
NONLINEAR SYSTEMS
SAMPLED-DATA
title_short Characterization of semiglobal stability properties for discrete-time models of non-uniformly sampled nonlinear systems
title_full Characterization of semiglobal stability properties for discrete-time models of non-uniformly sampled nonlinear systems
title_fullStr Characterization of semiglobal stability properties for discrete-time models of non-uniformly sampled nonlinear systems
title_full_unstemmed Characterization of semiglobal stability properties for discrete-time models of non-uniformly sampled nonlinear systems
title_sort Characterization of semiglobal stability properties for discrete-time models of non-uniformly sampled nonlinear systems
dc.creator.none.fl_str_mv Vallarella, Alexis Javier
Haimovich, Hernan
author Vallarella, Alexis Javier
author_facet Vallarella, Alexis Javier
Haimovich, Hernan
author_role author
author2 Haimovich, Hernan
author2_role author
dc.subject.none.fl_str_mv DISCRETE-TIME MODELS
INPUT-TO-STATE STABILITY (ISS)
NON-UNIFORM SAMPLING
NONLINEAR SYSTEMS
SAMPLED-DATA
topic DISCRETE-TIME MODELS
INPUT-TO-STATE STABILITY (ISS)
NON-UNIFORM SAMPLING
NONLINEAR SYSTEMS
SAMPLED-DATA
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.2
https://purl.org/becyt/ford/2
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Discrete-time models of non-uniformly sampled nonlinear systems under zero-order hold relate the next state sample to the current state sample, (constant) input value, and sampling interval. The exact discrete-time model, that is, the discrete-time model whose state matches that of the continuous-time nonlinear system at the sampling instants may be difficult or even impossible to obtain. In this context, one approach to the analysis of stability is based on the use of an approximate discrete-time model and a bound on the mismatch between the exact and approximate models. This approach requires three conceptually different tasks: (i) ensure the stability of the (approximate) discrete-time model, (ii) ensure that the stability of the approximate model carries over to the exact model, (iii) if necessary, bound intersample behaviour. Existing conditions for ensuring the stability of a discrete-time model as per task (i) have some or all of the following drawbacks: are only sufficient but not necessary; do not allow for varying sampling rate; cannot be applied in the presence of state-measurement or actuation errors. In this paper, we overcome these drawbacks by providing characterizations of, i.e. necessary and sufficient conditions for, two stability properties: semiglobal asymptotic stability, robustly with respect to bounded disturbances, and semiglobal input-to-state stability, where the (disturbance) input may successfully represent state-measurement or actuation errors. Our results can be applied when sampling is not necessarily uniform.
Fil: Vallarella, Alexis Javier. 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: 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
description Discrete-time models of non-uniformly sampled nonlinear systems under zero-order hold relate the next state sample to the current state sample, (constant) input value, and sampling interval. The exact discrete-time model, that is, the discrete-time model whose state matches that of the continuous-time nonlinear system at the sampling instants may be difficult or even impossible to obtain. In this context, one approach to the analysis of stability is based on the use of an approximate discrete-time model and a bound on the mismatch between the exact and approximate models. This approach requires three conceptually different tasks: (i) ensure the stability of the (approximate) discrete-time model, (ii) ensure that the stability of the approximate model carries over to the exact model, (iii) if necessary, bound intersample behaviour. Existing conditions for ensuring the stability of a discrete-time model as per task (i) have some or all of the following drawbacks: are only sufficient but not necessary; do not allow for varying sampling rate; cannot be applied in the presence of state-measurement or actuation errors. In this paper, we overcome these drawbacks by providing characterizations of, i.e. necessary and sufficient conditions for, two stability properties: semiglobal asymptotic stability, robustly with respect to bounded disturbances, and semiglobal input-to-state stability, where the (disturbance) input may successfully represent state-measurement or actuation errors. Our results can be applied when sampling is not necessarily uniform.
publishDate 2018
dc.date.none.fl_str_mv 2018-12
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/11336/87977
Vallarella, Alexis Javier; Haimovich, Hernan; Characterization of semiglobal stability properties for discrete-time models of non-uniformly sampled nonlinear systems; Elsevier Science; Systems And Control Letters; 122; 12-2018; 60-66
0167-6911
CONICET Digital
CONICET
url http://hdl.handle.net/11336/87977
identifier_str_mv Vallarella, Alexis Javier; Haimovich, Hernan; Characterization of semiglobal stability properties for discrete-time models of non-uniformly sampled nonlinear systems; Elsevier Science; Systems And Control Letters; 122; 12-2018; 60-66
0167-6911
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.sysconle.2018.10.005
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0167691118301798
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
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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