Ultimate boundedness sufficient conditions for nonlinear systems using TS fuzzy modelling
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1016/j.fss.2018.03.010 http://hdl.handle.net/11449/170819 |
Resumo: | Using Takagi–Sugeno (TS) fuzzy modelling, sufficient conditions to ensure ultimate boundedness of solutions of nonlinear switched systems are given. The sufficient conditions are given in terms of properties of invariant sets and of an auxiliary system formed by a convex combination of the switching subsystems. By exploring the results of this paper, estimates of the attractor and domain of attraction can be found even when (i) the derivative of an auxiliary function V, which plays the same role of a Lyapunov function, attains positive values in some sets and (ii) the solutions of each subsystem of the switched system are not necessarily ultimately bounded. The sufficient conditions are formulated as a problem of checking the feasibility of linear matrix inequalities (LMIs). Indeed, these LMIs provide a systematic procedure that can help to find auxiliary scalar Lyapunov-like functions for a class of switched nonlinear systems. A numerical example illustrates the effectiveness of the proposed approach in estimating attractors of nonlinear dynamic switched systems. |
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Ultimate boundedness sufficient conditions for nonlinear systems using TS fuzzy modellingInvariant setsSwitched systemsTS fuzzy modellingUltimate boundednessUsing Takagi–Sugeno (TS) fuzzy modelling, sufficient conditions to ensure ultimate boundedness of solutions of nonlinear switched systems are given. The sufficient conditions are given in terms of properties of invariant sets and of an auxiliary system formed by a convex combination of the switching subsystems. By exploring the results of this paper, estimates of the attractor and domain of attraction can be found even when (i) the derivative of an auxiliary function V, which plays the same role of a Lyapunov function, attains positive values in some sets and (ii) the solutions of each subsystem of the switched system are not necessarily ultimately bounded. The sufficient conditions are formulated as a problem of checking the feasibility of linear matrix inequalities (LMIs). Indeed, these LMIs provide a systematic procedure that can help to find auxiliary scalar Lyapunov-like functions for a class of switched nonlinear systems. A numerical example illustrates the effectiveness of the proposed approach in estimating attractors of nonlinear dynamic switched systems.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Universidade Tecnológica Federal do Paraná, Campus Cornélio ProcópioUniversidade Estadual Paulista (Unesp) Instituto de QuímicaUniversidade de São Paulo, Campus São CarlosUniversidade Estadual Paulista (Unesp) Instituto de QuímicaCNPq: 142246/2010-7CNPq: 305486/2013-6CNPq: 306477/2013-0CNPq: 448391/2014-7Universidade Tecnológica Federal do ParanáUniversidade Estadual Paulista (Unesp)Universidade de São Paulo (USP)Valentino, Michele C.Faria, Flávio A. [UNESP]Oliveira, Vilma A.Alberto, Luís F.C.2018-12-11T16:52:33Z2018-12-11T16:52:33Z2018-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://dx.doi.org/10.1016/j.fss.2018.03.010Fuzzy Sets and Systems.0165-0114http://hdl.handle.net/11449/17081910.1016/j.fss.2018.03.0102-s2.0-850443584272-s2.0-85044358427.pdfScopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengFuzzy Sets and Systems1,138info:eu-repo/semantics/openAccess2024-01-11T06:30:58Zoai:repositorio.unesp.br:11449/170819Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-01-11T06:30:58Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Ultimate boundedness sufficient conditions for nonlinear systems using TS fuzzy modelling |
title |
Ultimate boundedness sufficient conditions for nonlinear systems using TS fuzzy modelling |
spellingShingle |
Ultimate boundedness sufficient conditions for nonlinear systems using TS fuzzy modelling Valentino, Michele C. Invariant sets Switched systems TS fuzzy modelling Ultimate boundedness |
title_short |
Ultimate boundedness sufficient conditions for nonlinear systems using TS fuzzy modelling |
title_full |
Ultimate boundedness sufficient conditions for nonlinear systems using TS fuzzy modelling |
title_fullStr |
Ultimate boundedness sufficient conditions for nonlinear systems using TS fuzzy modelling |
title_full_unstemmed |
Ultimate boundedness sufficient conditions for nonlinear systems using TS fuzzy modelling |
title_sort |
Ultimate boundedness sufficient conditions for nonlinear systems using TS fuzzy modelling |
author |
Valentino, Michele C. |
author_facet |
Valentino, Michele C. Faria, Flávio A. [UNESP] Oliveira, Vilma A. Alberto, Luís F.C. |
author_role |
author |
author2 |
Faria, Flávio A. [UNESP] Oliveira, Vilma A. Alberto, Luís F.C. |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Universidade Tecnológica Federal do Paraná Universidade Estadual Paulista (Unesp) Universidade de São Paulo (USP) |
dc.contributor.author.fl_str_mv |
Valentino, Michele C. Faria, Flávio A. [UNESP] Oliveira, Vilma A. Alberto, Luís F.C. |
dc.subject.por.fl_str_mv |
Invariant sets Switched systems TS fuzzy modelling Ultimate boundedness |
topic |
Invariant sets Switched systems TS fuzzy modelling Ultimate boundedness |
description |
Using Takagi–Sugeno (TS) fuzzy modelling, sufficient conditions to ensure ultimate boundedness of solutions of nonlinear switched systems are given. The sufficient conditions are given in terms of properties of invariant sets and of an auxiliary system formed by a convex combination of the switching subsystems. By exploring the results of this paper, estimates of the attractor and domain of attraction can be found even when (i) the derivative of an auxiliary function V, which plays the same role of a Lyapunov function, attains positive values in some sets and (ii) the solutions of each subsystem of the switched system are not necessarily ultimately bounded. The sufficient conditions are formulated as a problem of checking the feasibility of linear matrix inequalities (LMIs). Indeed, these LMIs provide a systematic procedure that can help to find auxiliary scalar Lyapunov-like functions for a class of switched nonlinear systems. A numerical example illustrates the effectiveness of the proposed approach in estimating attractors of nonlinear dynamic switched systems. |
publishDate |
2018 |
dc.date.none.fl_str_mv |
2018-12-11T16:52:33Z 2018-12-11T16:52:33Z 2018-01-01 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1016/j.fss.2018.03.010 Fuzzy Sets and Systems. 0165-0114 http://hdl.handle.net/11449/170819 10.1016/j.fss.2018.03.010 2-s2.0-85044358427 2-s2.0-85044358427.pdf |
url |
http://dx.doi.org/10.1016/j.fss.2018.03.010 http://hdl.handle.net/11449/170819 |
identifier_str_mv |
Fuzzy Sets and Systems. 0165-0114 10.1016/j.fss.2018.03.010 2-s2.0-85044358427 2-s2.0-85044358427.pdf |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Fuzzy Sets and Systems 1,138 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1799965588594884608 |