Stochastic Stability for Markovian Jump Linear Systems Subject to a Crucial Failure Event

Detalhes bibliográficos
Autor(a) principal: Do Val, João B.R.
Data de Publicação: 2003
Outros Autores: Nespoli, Crisliane [UNESP]
Tipo de documento: Artigo de conferência
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1109/ACC.2003.1240503
http://hdl.handle.net/11449/67473
Resumo: This paper is concerned with the stability of discrete-time linear systems subject to random jumps in the parameters, described by an underlying finite-state Markov chain. In the model studied, a stopping time τ Δ is associated with the occurrence of a crucial failure after which the system is brought to a halt for maintenance. The usual stochastic stability concepts and associated results are not indicated, since they are tailored to pure infinite horizon problems. Using the concept named stochastic τ-stability, equivalent conditions to ensure the stochastic stability of the system until the occurrence of τ Δ is obtained. In addition, an intermediary and mixed case for which τ represents the minimum between the occurrence of a fix number N of failures and the occurrence of a crucial failure τ Δ is also considered. Necessary and sufficient conditions to ensure the stochastic τ-stability are provided in this setting that are auxiliary to the main result.
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spelling Stochastic Stability for Markovian Jump Linear Systems Subject to a Crucial Failure EventDiscrete time control systemsFailure (mechanical)Markov processesDiscrete-time linear systemsLinear systemsThis paper is concerned with the stability of discrete-time linear systems subject to random jumps in the parameters, described by an underlying finite-state Markov chain. In the model studied, a stopping time τ Δ is associated with the occurrence of a crucial failure after which the system is brought to a halt for maintenance. The usual stochastic stability concepts and associated results are not indicated, since they are tailored to pure infinite horizon problems. Using the concept named stochastic τ-stability, equivalent conditions to ensure the stochastic stability of the system until the occurrence of τ Δ is obtained. In addition, an intermediary and mixed case for which τ represents the minimum between the occurrence of a fix number N of failures and the occurrence of a crucial failure τ Δ is also considered. Necessary and sufficient conditions to ensure the stochastic τ-stability are provided in this setting that are auxiliary to the main result.UNICAMP-Univ. Est. de Campinas Fac. de Eng. Elétrica Depto. de Telemática, C.P. 6101, 13081-970 Campinas, SPUNESP-Univ. Est. Paulista Fac. de Ciências e Tecnologia, C.P. 467, 19060-900 Pres. Prudente, SPUNESP-Univ. Est. Paulista Fac. de Ciências e Tecnologia, C.P. 467, 19060-900 Pres. Prudente, SPUniversidade Estadual de Campinas (UNICAMP)Universidade Estadual Paulista (Unesp)Do Val, João B.R.Nespoli, Crisliane [UNESP]2014-05-27T11:20:56Z2014-05-27T11:20:56Z2003-11-07info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObject4249-4254http://dx.doi.org/10.1109/ACC.2003.1240503Proceedings of the American Control Conference, v. 5, p. 4249-4254.0743-1619http://hdl.handle.net/11449/6747310.1109/ACC.2003.12405032-s2.0-014216905269482537989528810000-0002-0690-0857Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengProceedings of the American Control Conference0,500info:eu-repo/semantics/openAccess2022-03-14T20:04:43Zoai:repositorio.unesp.br:11449/67473Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T18:04:39.784705Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Stochastic Stability for Markovian Jump Linear Systems Subject to a Crucial Failure Event
title Stochastic Stability for Markovian Jump Linear Systems Subject to a Crucial Failure Event
spellingShingle Stochastic Stability for Markovian Jump Linear Systems Subject to a Crucial Failure Event
Do Val, João B.R.
Discrete time control systems
Failure (mechanical)
Markov processes
Discrete-time linear systems
Linear systems
title_short Stochastic Stability for Markovian Jump Linear Systems Subject to a Crucial Failure Event
title_full Stochastic Stability for Markovian Jump Linear Systems Subject to a Crucial Failure Event
title_fullStr Stochastic Stability for Markovian Jump Linear Systems Subject to a Crucial Failure Event
title_full_unstemmed Stochastic Stability for Markovian Jump Linear Systems Subject to a Crucial Failure Event
title_sort Stochastic Stability for Markovian Jump Linear Systems Subject to a Crucial Failure Event
author Do Val, João B.R.
author_facet Do Val, João B.R.
Nespoli, Crisliane [UNESP]
author_role author
author2 Nespoli, Crisliane [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Universidade Estadual de Campinas (UNICAMP)
Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Do Val, João B.R.
Nespoli, Crisliane [UNESP]
dc.subject.por.fl_str_mv Discrete time control systems
Failure (mechanical)
Markov processes
Discrete-time linear systems
Linear systems
topic Discrete time control systems
Failure (mechanical)
Markov processes
Discrete-time linear systems
Linear systems
description This paper is concerned with the stability of discrete-time linear systems subject to random jumps in the parameters, described by an underlying finite-state Markov chain. In the model studied, a stopping time τ Δ is associated with the occurrence of a crucial failure after which the system is brought to a halt for maintenance. The usual stochastic stability concepts and associated results are not indicated, since they are tailored to pure infinite horizon problems. Using the concept named stochastic τ-stability, equivalent conditions to ensure the stochastic stability of the system until the occurrence of τ Δ is obtained. In addition, an intermediary and mixed case for which τ represents the minimum between the occurrence of a fix number N of failures and the occurrence of a crucial failure τ Δ is also considered. Necessary and sufficient conditions to ensure the stochastic τ-stability are provided in this setting that are auxiliary to the main result.
publishDate 2003
dc.date.none.fl_str_mv 2003-11-07
2014-05-27T11:20:56Z
2014-05-27T11:20:56Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/conferenceObject
format conferenceObject
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1109/ACC.2003.1240503
Proceedings of the American Control Conference, v. 5, p. 4249-4254.
0743-1619
http://hdl.handle.net/11449/67473
10.1109/ACC.2003.1240503
2-s2.0-0142169052
6948253798952881
0000-0002-0690-0857
url http://dx.doi.org/10.1109/ACC.2003.1240503
http://hdl.handle.net/11449/67473
identifier_str_mv Proceedings of the American Control Conference, v. 5, p. 4249-4254.
0743-1619
10.1109/ACC.2003.1240503
2-s2.0-0142169052
6948253798952881
0000-0002-0690-0857
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Proceedings of the American Control Conference
0,500
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 4249-4254
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
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