Polyhedral regions of local stability for linear discrete-time systems with saturating controls

Detalhes bibliográficos
Autor(a) principal: Silva Junior, Joao Manoel Gomes da
Data de Publicação: 1999
Outros Autores: Tarbouriech, Sophie
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFRGS
Texto Completo: http://hdl.handle.net/10183/27562
Resumo: The study and the determination of polyhedral regions of local stability for linear systems subject to control saturation is addressed. The analysis of the nonlinear behavior of the closed-loop saturated system is made by dividing the state space in regions of saturation. Inside each of these regions, the system evolution can be represented by a linear system with an additive disturbance. From this representation, a necessary and sufficient condition relative to the contractivity of a given convex compact polyhedral set is stated. Consequently, the polyhedral set can be associated with a Lyapunov function and the local asymptotic stability of the saturated closed-loop system inside the set is guaranteed. Furthermore, it is shown how, in some particular cases, the compactness condition can be relaxed in order to ensure the asymptotic stability in unbounded polyhedra. Finally, an application of the contractivity conditions is presented in order to determine local asymptotic stability regions for the closed-loop saturated system.
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spelling Silva Junior, Joao Manoel Gomes daTarbouriech, Sophie2011-01-28T05:59:03Z19990018-9286http://hdl.handle.net/10183/27562000293701The study and the determination of polyhedral regions of local stability for linear systems subject to control saturation is addressed. The analysis of the nonlinear behavior of the closed-loop saturated system is made by dividing the state space in regions of saturation. Inside each of these regions, the system evolution can be represented by a linear system with an additive disturbance. From this representation, a necessary and sufficient condition relative to the contractivity of a given convex compact polyhedral set is stated. Consequently, the polyhedral set can be associated with a Lyapunov function and the local asymptotic stability of the saturated closed-loop system inside the set is guaranteed. Furthermore, it is shown how, in some particular cases, the compactness condition can be relaxed in order to ensure the asymptotic stability in unbounded polyhedra. Finally, an application of the contractivity conditions is presented in order to determine local asymptotic stability regions for the closed-loop saturated system.application/pdfengIEEE Transactions on Automatic Control. New York. Vol. 44, no. 11 (Nov. 1999), p. 2081-2085Controle automático : EstabilidadeSistemas lineares : EstabilidadeContractivityControl saturationLocal stabilityLolyhedralLypunov functionPolyhedral regions of local stability for linear discrete-time systems with saturating controlsEstrangeiroinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSORIGINAL000293701.pdf000293701.pdfTexto completo (inglês)application/pdf176041http://www.lume.ufrgs.br/bitstream/10183/27562/1/000293701.pdf8c749df8370dc7fa05005201ab3e91deMD51TEXT000293701.pdf.txt000293701.pdf.txtExtracted Texttext/plain30146http://www.lume.ufrgs.br/bitstream/10183/27562/2/000293701.pdf.txt07fa557ddb81c88852d0d4e94dcd0977MD52THUMBNAIL000293701.pdf.jpg000293701.pdf.jpgGenerated Thumbnailimage/jpeg2045http://www.lume.ufrgs.br/bitstream/10183/27562/3/000293701.pdf.jpg1db06a0eb6d6b5d02cf069bcd0185ff2MD5310183/275622021-06-26 04:45:14.4972oai:www.lume.ufrgs.br:10183/27562Repositório de PublicaçõesPUBhttps://lume.ufrgs.br/oai/requestopendoar:2021-06-26T07:45:14Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false
dc.title.pt_BR.fl_str_mv Polyhedral regions of local stability for linear discrete-time systems with saturating controls
title Polyhedral regions of local stability for linear discrete-time systems with saturating controls
spellingShingle Polyhedral regions of local stability for linear discrete-time systems with saturating controls
Silva Junior, Joao Manoel Gomes da
Controle automático : Estabilidade
Sistemas lineares : Estabilidade
Contractivity
Control saturation
Local stability
Lolyhedral
Lypunov function
title_short Polyhedral regions of local stability for linear discrete-time systems with saturating controls
title_full Polyhedral regions of local stability for linear discrete-time systems with saturating controls
title_fullStr Polyhedral regions of local stability for linear discrete-time systems with saturating controls
title_full_unstemmed Polyhedral regions of local stability for linear discrete-time systems with saturating controls
title_sort Polyhedral regions of local stability for linear discrete-time systems with saturating controls
author Silva Junior, Joao Manoel Gomes da
author_facet Silva Junior, Joao Manoel Gomes da
Tarbouriech, Sophie
author_role author
author2 Tarbouriech, Sophie
author2_role author
dc.contributor.author.fl_str_mv Silva Junior, Joao Manoel Gomes da
Tarbouriech, Sophie
dc.subject.por.fl_str_mv Controle automático : Estabilidade
Sistemas lineares : Estabilidade
topic Controle automático : Estabilidade
Sistemas lineares : Estabilidade
Contractivity
Control saturation
Local stability
Lolyhedral
Lypunov function
dc.subject.eng.fl_str_mv Contractivity
Control saturation
Local stability
Lolyhedral
Lypunov function
description The study and the determination of polyhedral regions of local stability for linear systems subject to control saturation is addressed. The analysis of the nonlinear behavior of the closed-loop saturated system is made by dividing the state space in regions of saturation. Inside each of these regions, the system evolution can be represented by a linear system with an additive disturbance. From this representation, a necessary and sufficient condition relative to the contractivity of a given convex compact polyhedral set is stated. Consequently, the polyhedral set can be associated with a Lyapunov function and the local asymptotic stability of the saturated closed-loop system inside the set is guaranteed. Furthermore, it is shown how, in some particular cases, the compactness condition can be relaxed in order to ensure the asymptotic stability in unbounded polyhedra. Finally, an application of the contractivity conditions is presented in order to determine local asymptotic stability regions for the closed-loop saturated system.
publishDate 1999
dc.date.issued.fl_str_mv 1999
dc.date.accessioned.fl_str_mv 2011-01-28T05:59:03Z
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dc.identifier.uri.fl_str_mv http://hdl.handle.net/10183/27562
dc.identifier.issn.pt_BR.fl_str_mv 0018-9286
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dc.language.iso.fl_str_mv eng
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dc.relation.ispartof.pt_BR.fl_str_mv IEEE Transactions on Automatic Control. New York. Vol. 44, no. 11 (Nov. 1999), p. 2081-2085
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