Average reachability of continuous-time Markov jump linear systems and the linear minimum mean square estimator

. In this paper we study the average reachability gramian for continuous-time linear systems with additive noise and jump parameters driven by a general Markov chain. We define a rather natural reachability concept by requiring that the average reachability gramian be positive definite. Aiming at a...

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Autores:
Roa Narvaez, Alfredo Rafael
Fontoura Costa, Eduardo
Tipo de recurso:
Article of journal
Fecha de publicación:
2016
Institución:
Corporación Universidad de la Costa
Repositorio:
REDICUC - Repositorio CUC
Idioma:
eng
OAI Identifier:
oai:repositorio.cuc.edu.co:11323/1286
Acceso en línea:
https://hdl.handle.net/11323/1286
https://repositorio.cuc.edu.co/
Palabra clave:
Continuous-time systems
Filtering
Markov jump linear systems
Reachability of stochastic systems
Stochastic systems
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 the linear minimum mean square estimator
title Average reachability of continuous-time Markov jump linear systems and the linear minimum mean square estimator
spellingShingle Average reachability of continuous-time Markov jump linear systems and the linear minimum mean square estimator
Continuous-time systems
Filtering
Markov jump linear systems
Reachability of stochastic systems
Stochastic systems
title_short Average reachability of continuous-time Markov jump linear systems and the linear minimum mean square estimator
title_full Average reachability of continuous-time Markov jump linear systems and the linear minimum mean square estimator
title_fullStr Average reachability of continuous-time Markov jump linear systems and the linear minimum mean square estimator
title_full_unstemmed Average reachability of continuous-time Markov jump linear systems and the linear minimum mean square estimator
title_sort Average reachability of continuous-time Markov jump linear systems and the linear minimum mean square estimator
dc.creator.fl_str_mv Roa Narvaez, Alfredo Rafael
Fontoura Costa, Eduardo
dc.contributor.author.spa.fl_str_mv Roa Narvaez, Alfredo Rafael
Fontoura Costa, Eduardo
dc.subject.eng.fl_str_mv Continuous-time systems
Filtering
Markov jump linear systems
Reachability of stochastic systems
Stochastic systems
topic Continuous-time systems
Filtering
Markov jump linear systems
Reachability of stochastic systems
Stochastic systems
description . In this paper we study the average reachability gramian for continuous-time linear systems with additive noise and jump parameters driven by a general Markov chain. We define a rather natural reachability concept by requiring that the average reachability gramian be positive definite. Aiming at a testable condition, we introduce a set of reachability matrices for this class of systems and employ invariance properties of the null space of the noise coefficient matrices to show that the system is reachable if and only if these matrices are of full rank. We also show for reachable systems that the state second moment is positive definite. One consequence of this result in the context of linear minimum mean square state estimation for reachable systems is that the expectation of the error covariance matrix is positive definite. Moreover, the average boundedness of the error covariance matrix is invariant to a type of perturbation in the noise model, meaning that the estimates are not overly sensitive, which consists in a property that is desirable in applications and sometimes referred to as stability of the estimator.
publishDate 2016
dc.date.issued.none.fl_str_mv 2016
dc.date.accessioned.none.fl_str_mv 2018-11-19T13:24:54Z
dc.date.available.none.fl_str_mv 2018-11-19T13:24:54Z
dc.type.spa.fl_str_mv Artículo de revista
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.coar.spa.fl_str_mv http://purl.org/coar/resource_type/c_6501
dc.type.content.spa.fl_str_mv Text
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/article
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dc.identifier.issn.spa.fl_str_mv 03630129
dc.identifier.uri.spa.fl_str_mv https://hdl.handle.net/11323/1286
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 03630129
Corporación Universidad de la Costa
REDICUC - Repositorio CUC
url https://hdl.handle.net/11323/1286
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 SIAM Journal on Control and Optimization
institution Corporación Universidad de la Costa
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spelling Roa Narvaez, Alfredo RafaelFontoura Costa, Eduardo2018-11-19T13:24:54Z2018-11-19T13:24:54Z201603630129https://hdl.handle.net/11323/1286Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/. In this paper we study the average reachability gramian for continuous-time linear systems with additive noise and jump parameters driven by a general Markov chain. We define a rather natural reachability concept by requiring that the average reachability gramian be positive definite. Aiming at a testable condition, we introduce a set of reachability matrices for this class of systems and employ invariance properties of the null space of the noise coefficient matrices to show that the system is reachable if and only if these matrices are of full rank. We also show for reachable systems that the state second moment is positive definite. One consequence of this result in the context of linear minimum mean square state estimation for reachable systems is that the expectation of the error covariance matrix is positive definite. Moreover, the average boundedness of the error covariance matrix is invariant to a type of perturbation in the noise model, meaning that the estimates are not overly sensitive, which consists in a property that is desirable in applications and sometimes referred to as stability of the estimator.Roa Narvaez, Alfredo Rafael-a701a283-5910-4c8b-a74e-6554527e3b15-600Fontoura Costa, Eduardo-f549c51c-f93f-4815-9533-836811e280fa-600engSIAM Journal on Control and OptimizationAtribución – No comercial – Compartir igualinfo:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Continuous-time systemsFilteringMarkov jump linear systemsReachability of stochastic systemsStochastic systemsAverage reachability of continuous-time Markov jump linear systems and the linear minimum mean square estimatorArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/acceptedVersionPublicationORIGINALAverage reachability of continuous-time Markov jump linear.pdfAverage reachability of continuous-time Markov jump linear.pdfapplication/pdf735562https://repositorio.cuc.edu.co/bitstreams/737ea18e-a67b-4bb7-adf6-853ae4dc43d5/download2b88ec7fe0b9ddd2ad546e85b52cde07MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://repositorio.cuc.edu.co/bitstreams/f923ed2f-c7fd-495a-8dfd-9c67ef2ce6b5/download8a4605be74aa9ea9d79846c1fba20a33MD52THUMBNAILAverage reachability of continuous-time Markov jump linear.pdf.jpgAverage reachability of continuous-time Markov jump linear.pdf.jpgimage/jpeg56383https://repositorio.cuc.edu.co/bitstreams/71f97c81-8b91-4a7f-ad95-0195741bce5a/download10fc49325df07b973e488a175606b3a6MD54TEXTAverage reachability of continuous-time Markov jump linear.pdf.txtAverage reachability of continuous-time Markov jump linear.pdf.txttext/plain83059https://repositorio.cuc.edu.co/bitstreams/3ce7360c-0abf-4de9-aec1-9aa570ef3fe3/downloada93668353a63be7c085576b52e6635f6MD5511323/1286oai:repositorio.cuc.edu.co:11323/12862024-09-17 12:46:42.231open.accesshttps://repositorio.cuc.edu.coRepositorio de la Universidad de la Costa CUCrepdigital@cuc.edu.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