Piecewise Implicit Differential Systems
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1007/s10884-016-9538-2 http://hdl.handle.net/11449/168710 |
Resumo: | In this article we deal with non-smooth dynamical systems expressed by a piecewise first order implicit differential equations of the form x˙=1,(y˙)2={g1(x,y)ifφ(x,y)≥0g2(x,y)ifφ(x,y)≤0,where g1, g2, φ: U→ R are smooth functions and U⊆ R2 is an open set. The main concern is to study sliding modes of such systems around some typical singularities. The novelty of our approach is that some singular perturbation problems of the form x˙=f(x,y,ε),(εy˙)2=g(x,y,ε)arise when the Sotomayor–Teixeira regularization is applied with (x, y) ∈ U , ε≥ 0 , and f, g smooth in all variables. |
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Repositório Institucional da UNESP |
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Piecewise Implicit Differential SystemsImplicit differential equationNon-smooth dynamical systemSingular perturbationSliding vector fieldsIn this article we deal with non-smooth dynamical systems expressed by a piecewise first order implicit differential equations of the form x˙=1,(y˙)2={g1(x,y)ifφ(x,y)≥0g2(x,y)ifφ(x,y)≤0,where g1, g2, φ: U→ R are smooth functions and U⊆ R2 is an open set. The main concern is to study sliding modes of such systems around some typical singularities. The novelty of our approach is that some singular perturbation problems of the form x˙=f(x,y,ε),(εy˙)2=g(x,y,ε)arise when the Sotomayor–Teixeira regularization is applied with (x, y) ∈ U , ε≥ 0 , and f, g smooth in all variables.IBILCE–UNESP, Rua C. Colombo, 2265IMECC–UNICAMPUFSCARIBILCE–UNESP, Rua C. Colombo, 2265Universidade Estadual Paulista (Unesp)Universidade Estadual de Campinas (UNICAMP)Universidade Federal de São Carlos (UFSCar)Lopes, Bruno D. [UNESP]da Silva, Paulo R. [UNESP]Teixeira, Marco A.2018-12-11T16:42:39Z2018-12-11T16:42:39Z2017-12-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1519-1537application/pdfhttp://dx.doi.org/10.1007/s10884-016-9538-2Journal of Dynamics and Differential Equations, v. 29, n. 4, p. 1519-1537, 2017.1572-92221040-7294http://hdl.handle.net/11449/16871010.1007/s10884-016-9538-22-s2.0-849731373892-s2.0-84973137389.pdfScopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Dynamics and Differential Equations1,208info:eu-repo/semantics/openAccess2023-12-09T06:19:51Zoai:repositorio.unesp.br:11449/168710Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T19:50:58.099827Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Piecewise Implicit Differential Systems |
title |
Piecewise Implicit Differential Systems |
spellingShingle |
Piecewise Implicit Differential Systems Lopes, Bruno D. [UNESP] Implicit differential equation Non-smooth dynamical system Singular perturbation Sliding vector fields |
title_short |
Piecewise Implicit Differential Systems |
title_full |
Piecewise Implicit Differential Systems |
title_fullStr |
Piecewise Implicit Differential Systems |
title_full_unstemmed |
Piecewise Implicit Differential Systems |
title_sort |
Piecewise Implicit Differential Systems |
author |
Lopes, Bruno D. [UNESP] |
author_facet |
Lopes, Bruno D. [UNESP] da Silva, Paulo R. [UNESP] Teixeira, Marco A. |
author_role |
author |
author2 |
da Silva, Paulo R. [UNESP] Teixeira, Marco A. |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) Universidade Estadual de Campinas (UNICAMP) Universidade Federal de São Carlos (UFSCar) |
dc.contributor.author.fl_str_mv |
Lopes, Bruno D. [UNESP] da Silva, Paulo R. [UNESP] Teixeira, Marco A. |
dc.subject.por.fl_str_mv |
Implicit differential equation Non-smooth dynamical system Singular perturbation Sliding vector fields |
topic |
Implicit differential equation Non-smooth dynamical system Singular perturbation Sliding vector fields |
description |
In this article we deal with non-smooth dynamical systems expressed by a piecewise first order implicit differential equations of the form x˙=1,(y˙)2={g1(x,y)ifφ(x,y)≥0g2(x,y)ifφ(x,y)≤0,where g1, g2, φ: U→ R are smooth functions and U⊆ R2 is an open set. The main concern is to study sliding modes of such systems around some typical singularities. The novelty of our approach is that some singular perturbation problems of the form x˙=f(x,y,ε),(εy˙)2=g(x,y,ε)arise when the Sotomayor–Teixeira regularization is applied with (x, y) ∈ U , ε≥ 0 , and f, g smooth in all variables. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-12-01 2018-12-11T16:42:39Z 2018-12-11T16:42:39Z |
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/10.1007/s10884-016-9538-2 Journal of Dynamics and Differential Equations, v. 29, n. 4, p. 1519-1537, 2017. 1572-9222 1040-7294 http://hdl.handle.net/11449/168710 10.1007/s10884-016-9538-2 2-s2.0-84973137389 2-s2.0-84973137389.pdf |
url |
http://dx.doi.org/10.1007/s10884-016-9538-2 http://hdl.handle.net/11449/168710 |
identifier_str_mv |
Journal of Dynamics and Differential Equations, v. 29, n. 4, p. 1519-1537, 2017. 1572-9222 1040-7294 10.1007/s10884-016-9538-2 2-s2.0-84973137389 2-s2.0-84973137389.pdf |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Journal of Dynamics and Differential Equations 1,208 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
1519-1537 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_ |
1808129128279310336 |