Stochastic stability for Markovian jump linear systems associated with a finite number of jump times
Autor(a) principal: | |
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Data de Publicação: | 2003 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1016/S0022-247X(03)00424-4 http://hdl.handle.net/11449/7088 |
Resumo: | This paper deals with a stochastic stability concept for discrete-time Markovian jump linear systems. The random jump parameter is associated to changes between the system operation modes due to failures or repairs, which can be well described by an underlying finite-state Markov chain. In the model studied, a fixed number of failures or repairs is allowed, after which, the system is brought to a halt for maintenance or for replacement. The usual concepts of stochastic stability are related to pure infinite horizon problems, and are not appropriate in this scenario. A new stability concept is introduced, named stochastic tau-stability that is tailored to the present setting. Necessary and sufficient conditions to ensure the stochastic tau-stability are provided, and the almost sure stability concept associated with this class of processes is also addressed. The paper also develops equivalences among second order concepts that parallels the results for infinite horizon problems. (C) 2003 Elsevier B.V. All rights reserved. |
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Repositório Institucional da UNESP |
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Stochastic stability for Markovian jump linear systems associated with a finite number of jump timesMarkov jump linear systemsstochastic stabilitymaintenance modelThis paper deals with a stochastic stability concept for discrete-time Markovian jump linear systems. The random jump parameter is associated to changes between the system operation modes due to failures or repairs, which can be well described by an underlying finite-state Markov chain. In the model studied, a fixed number of failures or repairs is allowed, after which, the system is brought to a halt for maintenance or for replacement. The usual concepts of stochastic stability are related to pure infinite horizon problems, and are not appropriate in this scenario. A new stability concept is introduced, named stochastic tau-stability that is tailored to the present setting. Necessary and sufficient conditions to ensure the stochastic tau-stability are provided, and the almost sure stability concept associated with this class of processes is also addressed. The paper also develops equivalences among second order concepts that parallels the results for infinite horizon problems. (C) 2003 Elsevier B.V. All rights reserved.Univ Estadual Campinas, UNICAMP, Fac Elect Engn, Dept Telemat, BR-13081970 Campinas, SP, BrazilUniv Estadual Paulista, UNESP, Fac Ciências & Tecnol, Dept Matemat, BR-19060400 Pres Prudente, SP, BrazilUniv Estadual Paulista, UNESP, Fac Ciências & Tecnol, Dept Matemat, BR-19060400 Pres Prudente, SP, BrazilElsevier B.V.Universidade Estadual de Campinas (UNICAMP)Universidade Estadual Paulista (Unesp)do Val, JBRNespoli, C.Caceres, YRZ2014-05-20T13:23:29Z2014-05-20T13:23:29Z2003-09-15info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article551-563application/pdfhttp://dx.doi.org/10.1016/S0022-247X(03)00424-4Journal of Mathematical Analysis and Applications. San Diego: Academic Press Inc. Elsevier B.V., v. 285, n. 2, p. 551-563, 2003.0022-247Xhttp://hdl.handle.net/11449/708810.1016/S0022-247X(03)00424-4WOS:000185398300016WOS000185398300016.pdf69482537989528810000-0002-0690-0857Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Mathematical Analysis and Applications1.138info:eu-repo/semantics/openAccess2024-06-19T14:32:04Zoai:repositorio.unesp.br:11449/7088Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-06-19T14:32:04Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Stochastic stability for Markovian jump linear systems associated with a finite number of jump times |
title |
Stochastic stability for Markovian jump linear systems associated with a finite number of jump times |
spellingShingle |
Stochastic stability for Markovian jump linear systems associated with a finite number of jump times do Val, JBR Markov jump linear systems stochastic stability maintenance model |
title_short |
Stochastic stability for Markovian jump linear systems associated with a finite number of jump times |
title_full |
Stochastic stability for Markovian jump linear systems associated with a finite number of jump times |
title_fullStr |
Stochastic stability for Markovian jump linear systems associated with a finite number of jump times |
title_full_unstemmed |
Stochastic stability for Markovian jump linear systems associated with a finite number of jump times |
title_sort |
Stochastic stability for Markovian jump linear systems associated with a finite number of jump times |
author |
do Val, JBR |
author_facet |
do Val, JBR Nespoli, C. Caceres, YRZ |
author_role |
author |
author2 |
Nespoli, C. Caceres, YRZ |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual de Campinas (UNICAMP) Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
do Val, JBR Nespoli, C. Caceres, YRZ |
dc.subject.por.fl_str_mv |
Markov jump linear systems stochastic stability maintenance model |
topic |
Markov jump linear systems stochastic stability maintenance model |
description |
This paper deals with a stochastic stability concept for discrete-time Markovian jump linear systems. The random jump parameter is associated to changes between the system operation modes due to failures or repairs, which can be well described by an underlying finite-state Markov chain. In the model studied, a fixed number of failures or repairs is allowed, after which, the system is brought to a halt for maintenance or for replacement. The usual concepts of stochastic stability are related to pure infinite horizon problems, and are not appropriate in this scenario. A new stability concept is introduced, named stochastic tau-stability that is tailored to the present setting. Necessary and sufficient conditions to ensure the stochastic tau-stability are provided, and the almost sure stability concept associated with this class of processes is also addressed. The paper also develops equivalences among second order concepts that parallels the results for infinite horizon problems. (C) 2003 Elsevier B.V. All rights reserved. |
publishDate |
2003 |
dc.date.none.fl_str_mv |
2003-09-15 2014-05-20T13:23:29Z 2014-05-20T13:23:29Z |
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/S0022-247X(03)00424-4 Journal of Mathematical Analysis and Applications. San Diego: Academic Press Inc. Elsevier B.V., v. 285, n. 2, p. 551-563, 2003. 0022-247X http://hdl.handle.net/11449/7088 10.1016/S0022-247X(03)00424-4 WOS:000185398300016 WOS000185398300016.pdf 6948253798952881 0000-0002-0690-0857 |
url |
http://dx.doi.org/10.1016/S0022-247X(03)00424-4 http://hdl.handle.net/11449/7088 |
identifier_str_mv |
Journal of Mathematical Analysis and Applications. San Diego: Academic Press Inc. Elsevier B.V., v. 285, n. 2, p. 551-563, 2003. 0022-247X 10.1016/S0022-247X(03)00424-4 WOS:000185398300016 WOS000185398300016.pdf 6948253798952881 0000-0002-0690-0857 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Journal of Mathematical Analysis and Applications 1.138 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
551-563 application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier B.V. |
publisher.none.fl_str_mv |
Elsevier B.V. |
dc.source.none.fl_str_mv |
Web of Science 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_ |
1803045387205869568 |