Average reachability of continuous-time Markov jump linear systems and linear Markovian state observers

Stability of state estimators for Markov jump linear systems featuring time-varying and correlated noise processes are studied in this paper. Three conditions for stability are presented, starting with a more general one requiring positiveness of the covariance of the error estimate, and is applicab...

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Autores:
Narvaez Alfredo, Roa Rafael
Costa, Eduardo Fontoura
Tipo de recurso:
http://purl.org/coar/resource_type/c_f744
Fecha de publicación:
2018
Institución:
Corporación Universidad de la Costa
Repositorio:
REDICUC - Repositorio CUC
Idioma:
eng
OAI Identifier:
oai:repositorio.cuc.edu.co:11323/1672
Acceso en línea:
https://hdl.handle.net/11323/1672
https://repositorio.cuc.edu.co/
Palabra clave:
Additive noise
Linear systems
Markov processes
State estimation
Rights
openAccess
License
Atribución – No comercial – Compartir igual
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dc.title.eng.fl_str_mv Average reachability of continuous-time Markov jump linear systems and linear Markovian state observers
title Average reachability of continuous-time Markov jump linear systems and linear Markovian state observers
spellingShingle Average reachability of continuous-time Markov jump linear systems and linear Markovian state observers
Additive noise
Linear systems
Markov processes
State estimation
title_short Average reachability of continuous-time Markov jump linear systems and linear Markovian state observers
title_full Average reachability of continuous-time Markov jump linear systems and linear Markovian state observers
title_fullStr Average reachability of continuous-time Markov jump linear systems and linear Markovian state observers
title_full_unstemmed Average reachability of continuous-time Markov jump linear systems and linear Markovian state observers
title_sort Average reachability of continuous-time Markov jump linear systems and linear Markovian state observers
dc.creator.fl_str_mv Narvaez Alfredo, Roa Rafael
Costa, Eduardo Fontoura
dc.contributor.author.spa.fl_str_mv Narvaez Alfredo, Roa Rafael
Costa, Eduardo Fontoura
dc.subject.eng.fl_str_mv Additive noise
Linear systems
Markov processes
State estimation
topic Additive noise
Linear systems
Markov processes
State estimation
description Stability of state estimators for Markov jump linear systems featuring time-varying and correlated noise processes are studied in this paper. Three conditions for stability are presented, starting with a more general one requiring positiveness of the covariance of the error estimate, and is applicable to a class of filters that contains the well known linear minimum mean square estimators. It is then derived a more strict condition based on the plant parameters only, which may be interpreted as requiring that the state additive noise pervades every system dynamics. Finally, we consider a structural notion linked with the reachability gramian and we show it is a sufficient condition for the previous ones to be fulfilled, thus linking the filter stability with the structure of the plant, and present a simple rank test. Illustrative examples are included.
publishDate 2018
dc.date.accessioned.none.fl_str_mv 2018-11-21T20:37:51Z
dc.date.available.none.fl_str_mv 2018-11-21T20:37:51Z
dc.date.issued.none.fl_str_mv 2018
dc.type.spa.fl_str_mv Documento de Conferencia
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_c94f
dc.type.coar.spa.fl_str_mv http://purl.org/coar/resource_type/c_f744
dc.type.content.spa.fl_str_mv Text
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/conferenceObject
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dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
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dc.identifier.isbn.spa.fl_str_mv 978-150902873-3
dc.identifier.uri.spa.fl_str_mv https://hdl.handle.net/11323/1672
dc.identifier.doi.spa.fl_str_mv DOI: 10.1109/CDC.2017.8264104
dc.identifier.instname.spa.fl_str_mv Corporación Universidad de la Costa
dc.identifier.reponame.spa.fl_str_mv REDICUC - Repositorio CUC
dc.identifier.repourl.spa.fl_str_mv https://repositorio.cuc.edu.co/
identifier_str_mv 978-150902873-3
DOI: 10.1109/CDC.2017.8264104
Corporación Universidad de la Costa
REDICUC - Repositorio CUC
url https://hdl.handle.net/11323/1672
https://repositorio.cuc.edu.co/
dc.language.iso.none.fl_str_mv eng
language eng
dc.rights.spa.fl_str_mv Atribución – No comercial – Compartir igual
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
dc.rights.coar.spa.fl_str_mv http://purl.org/coar/access_right/c_abf2
rights_invalid_str_mv Atribución – No comercial – Compartir igual
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.publisher.spa.fl_str_mv 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
institution Corporación Universidad de la Costa
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spelling Narvaez Alfredo, Roa RafaelCosta, Eduardo Fontoura2018-11-21T20:37:51Z2018-11-21T20:37:51Z2018978-150902873-3https://hdl.handle.net/11323/1672DOI: 10.1109/CDC.2017.8264104Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/Stability of state estimators for Markov jump linear systems featuring time-varying and correlated noise processes are studied in this paper. Three conditions for stability are presented, starting with a more general one requiring positiveness of the covariance of the error estimate, and is applicable to a class of filters that contains the well known linear minimum mean square estimators. It is then derived a more strict condition based on the plant parameters only, which may be interpreted as requiring that the state additive noise pervades every system dynamics. Finally, we consider a structural notion linked with the reachability gramian and we show it is a sufficient condition for the previous ones to be fulfilled, thus linking the filter stability with the structure of the plant, and present a simple rank test. Illustrative examples are included.Narvaez Alfredo, Roa Rafael-694e9b0e-6bff-4a2b-86f8-e3731c2a459d-0Costa, Eduardo Fontoura-8b55ed20-17d3-4c88-a1e6-b16b91283679-0eng2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017Atribución – No comercial – Compartir igualinfo:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Additive noiseLinear systemsMarkov processesState estimationAverage reachability of continuous-time Markov jump linear systems and linear Markovian state observersDocumento de Conferenciahttp://purl.org/coar/resource_type/c_f744http://purl.org/coar/resource_type/c_c94fTextinfo:eu-repo/semantics/conferenceObjecthttp://purl.org/redcol/resource_type/ECinfo:eu-repo/semantics/acceptedVersionPublicationLICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://repositorio.cuc.edu.co/bitstreams/a6005bb4-d33e-4328-977e-4aa7ea964684/download8a4605be74aa9ea9d79846c1fba20a33MD52ORIGINALAverage reachability of continuous.pdfAverage reachability of continuous.pdfapplication/pdf7171https://repositorio.cuc.edu.co/bitstreams/b09f4c26-2cfe-473f-9689-80cb26b13c48/downloadf51079ec09f3b510efefef53731b2504MD51THUMBNAILAverage reachability of continuous.pdf.jpgAverage reachability of continuous.pdf.jpgimage/jpeg36614https://repositorio.cuc.edu.co/bitstreams/a7de70dc-7c9f-4644-b170-4c32f4c49740/download9f886f35a7b49306f647a56f866e21beMD54TEXTAverage reachability of continuous.pdf.txtAverage reachability of continuous.pdf.txttext/plain1137https://repositorio.cuc.edu.co/bitstreams/8a09f89b-40d6-4fb1-9c8a-1bbd2f02cbe0/download9137dc363398278d1ecf23af3ef14211MD5511323/1672oai:repositorio.cuc.edu.co:11323/16722024-09-17 11:01:04.476open.accesshttps://repositorio.cuc.edu.coRepositorio de la Universidad de la Costa CUCrepdigital@cuc.edu.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