Stochastic stability for Markovian jump linear systems associated with a finite number of jump times

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...

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Detalhes bibliográficos
Autores: do Val, JBR, Nespoli, C., Caceres, YRZ
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2003
País:Brasil
Recursos:Universidade Estadual Paulista (UNESP)
Repositório:Repositório Institucional da UNESP
Idioma:inglês
OAI Identifier:oai:repositorio.unesp.br:11449/7088
Acesso em linha:http://dx.doi.org/10.1016/S0022-247X(03)00424-4
http://hdl.handle.net/11449/7088
Access Level:Acceso aberto
Palavra-chave:Markov jump linear systems
stochastic stability
maintenance model
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spelling 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)2014-05-20T13:23:29Z2014-05-20T13:23:29Z2003-09-15info: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/openAccessdo Val, JBRNespoli, C.Caceres, YRZ2025-10-22T17:04:00Zoai:repositorio.unesp.br:11449/7088Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestrepositoriounesp@unesp.bropendoar:29462025-10-22T17:04Repositório 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
dc.creator.none.fl_str_mv do Val, JBR
Nespoli, C.
Caceres, YRZ
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.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 repositoriounesp@unesp.br
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score 15,301603

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