Sufficient conditions in terms of linear matrix inequalities for guaranteed ultimately boundedness of solutions of switched Takagi-Sugeno fuzzy systems using the S-procedure
Autor(a) principal: | |
---|---|
Data de Publicação: | 2021 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1016/j.ins.2021.04.103 http://hdl.handle.net/11449/221861 |
Resumo: | In this paper, sufficient conditions to ensure the existence of a switching law that makes the solutions of switched Takagi-Sugeno (TS) fuzzy systems ultimately bounded are developed by means of linear matrix inequalities (LMIs). These LMIs are based on the existence of a scalar function, which plays a role similar to Lyapunov energy functions for an auxiliary system formed by a convex combination of all subsystems of the switched system. A feature of the developed results is that the derivatives of the scalar function can assume positive values in a bounded set described as level sets. The LMIs explore the S-procedure to obtain low levels of conservativeness and do not require the calculation of the derivative of the membership functions, which facilitates their application to switched TS fuzzy systems with many rules. Exploring the proposed conditions, we estimated the attractor and basin of attraction of some examples of switched TS fuzzy systems under a measurable switching law. These numerical examples showed the effectiveness of the proposed approach in maximizing the estimation of the bounded attraction domain. |
id |
UNSP_eb9f91ea6fecbaed37e96d837d141a96 |
---|---|
oai_identifier_str |
oai:repositorio.unesp.br:11449/221861 |
network_acronym_str |
UNSP |
network_name_str |
Repositório Institucional da UNESP |
repository_id_str |
2946 |
spelling |
Sufficient conditions in terms of linear matrix inequalities for guaranteed ultimately boundedness of solutions of switched Takagi-Sugeno fuzzy systems using the S-procedureless conservative conditionsLMIsSwitched TS fuzzy systemultimate boundedness conditionsIn this paper, sufficient conditions to ensure the existence of a switching law that makes the solutions of switched Takagi-Sugeno (TS) fuzzy systems ultimately bounded are developed by means of linear matrix inequalities (LMIs). These LMIs are based on the existence of a scalar function, which plays a role similar to Lyapunov energy functions for an auxiliary system formed by a convex combination of all subsystems of the switched system. A feature of the developed results is that the derivatives of the scalar function can assume positive values in a bounded set described as level sets. The LMIs explore the S-procedure to obtain low levels of conservativeness and do not require the calculation of the derivative of the membership functions, which facilitates their application to switched TS fuzzy systems with many rules. Exploring the proposed conditions, we estimated the attractor and basin of attraction of some examples of switched TS fuzzy systems under a measurable switching law. These numerical examples showed the effectiveness of the proposed approach in maximizing the estimation of the bounded attraction domain.Depto Acadêmico de Matemática Universidade Tecnológica Federal do Paraná (UTFPR)Depto de Matemática Universidade Estadual Paulista (Unesp), Escola de EngenhariaDepto de Engenharia Elétrica e Computação Escola de Engenharia de São Carlos Universidade de São PauloDepto de Matemática Universidade Estadual Paulista (Unesp), Escola de EngenhariaUniversidade Tecnológica Federal do Paraná (UTFPR)Universidade Estadual Paulista (UNESP)Universidade de São Paulo (USP)Valentino, Michele C.Faria, Flávio A. [UNESP]Oliveira, Vilma A.Alberto, Luís F.C.2022-04-28T19:40:59Z2022-04-28T19:40:59Z2021-09-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article501-521http://dx.doi.org/10.1016/j.ins.2021.04.103Information Sciences, v. 572, p. 501-521.0020-0255http://hdl.handle.net/11449/22186110.1016/j.ins.2021.04.1032-s2.0-85108856488Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengInformation Sciencesinfo:eu-repo/semantics/openAccess2022-04-28T19:40:59Zoai:repositorio.unesp.br:11449/221861Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T14:01:37.126992Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Sufficient conditions in terms of linear matrix inequalities for guaranteed ultimately boundedness of solutions of switched Takagi-Sugeno fuzzy systems using the S-procedure |
title |
Sufficient conditions in terms of linear matrix inequalities for guaranteed ultimately boundedness of solutions of switched Takagi-Sugeno fuzzy systems using the S-procedure |
spellingShingle |
Sufficient conditions in terms of linear matrix inequalities for guaranteed ultimately boundedness of solutions of switched Takagi-Sugeno fuzzy systems using the S-procedure Valentino, Michele C. less conservative conditions LMIs Switched TS fuzzy system ultimate boundedness conditions |
title_short |
Sufficient conditions in terms of linear matrix inequalities for guaranteed ultimately boundedness of solutions of switched Takagi-Sugeno fuzzy systems using the S-procedure |
title_full |
Sufficient conditions in terms of linear matrix inequalities for guaranteed ultimately boundedness of solutions of switched Takagi-Sugeno fuzzy systems using the S-procedure |
title_fullStr |
Sufficient conditions in terms of linear matrix inequalities for guaranteed ultimately boundedness of solutions of switched Takagi-Sugeno fuzzy systems using the S-procedure |
title_full_unstemmed |
Sufficient conditions in terms of linear matrix inequalities for guaranteed ultimately boundedness of solutions of switched Takagi-Sugeno fuzzy systems using the S-procedure |
title_sort |
Sufficient conditions in terms of linear matrix inequalities for guaranteed ultimately boundedness of solutions of switched Takagi-Sugeno fuzzy systems using the S-procedure |
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 (UTFPR) 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 |
less conservative conditions LMIs Switched TS fuzzy system ultimate boundedness conditions |
topic |
less conservative conditions LMIs Switched TS fuzzy system ultimate boundedness conditions |
description |
In this paper, sufficient conditions to ensure the existence of a switching law that makes the solutions of switched Takagi-Sugeno (TS) fuzzy systems ultimately bounded are developed by means of linear matrix inequalities (LMIs). These LMIs are based on the existence of a scalar function, which plays a role similar to Lyapunov energy functions for an auxiliary system formed by a convex combination of all subsystems of the switched system. A feature of the developed results is that the derivatives of the scalar function can assume positive values in a bounded set described as level sets. The LMIs explore the S-procedure to obtain low levels of conservativeness and do not require the calculation of the derivative of the membership functions, which facilitates their application to switched TS fuzzy systems with many rules. Exploring the proposed conditions, we estimated the attractor and basin of attraction of some examples of switched TS fuzzy systems under a measurable switching law. These numerical examples showed the effectiveness of the proposed approach in maximizing the estimation of the bounded attraction domain. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-09-01 2022-04-28T19:40:59Z 2022-04-28T19:40:59Z |
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.ins.2021.04.103 Information Sciences, v. 572, p. 501-521. 0020-0255 http://hdl.handle.net/11449/221861 10.1016/j.ins.2021.04.103 2-s2.0-85108856488 |
url |
http://dx.doi.org/10.1016/j.ins.2021.04.103 http://hdl.handle.net/11449/221861 |
identifier_str_mv |
Information Sciences, v. 572, p. 501-521. 0020-0255 10.1016/j.ins.2021.04.103 2-s2.0-85108856488 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Information Sciences |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
501-521 |
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_ |
1808128218177208320 |