Analysis of the stability of linear systems with continuous Markovian jumps

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In this paper analyzed the stability of linear systems with continuous Markovian jumps. Firstly, the conditions for the Markov chain to be homogeneous and the state space is finite are imposed. Then the types of stability are presented, for example quadratic average stability, stochastic stability,...

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Detalles Bibliográficos
Autores: Mayta Guillermo, Jorge Enrique, Echegaray Castillo, William C., Berrospi Zapana, Martin E.
Formato: artículo
Fecha de Publicación:2020
Institución:Universidad Nacional de Trujillo
Repositorio:Revistas - Universidad Nacional de Trujillo
Lenguaje:español
OAI Identifier:oai:ojs.revistas.unitru.edu.pe:article/2973
Enlace del recurso:https://revistas.unitru.edu.pe/index.php/SSMM/article/view/2973
Nivel de acceso:acceso abierto
Materia:Linear systems
Markov chain
Lyapunov equation and stability
Sistemas lineales
cadena de Markov
ecuación de Lyapunov y estabilidad
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spelling Analysis of the stability of linear systems with continuous Markovian jumpsAnálisis de la estabilidad de los sistemas lineales con saltos markovianos en tiempo continuoMayta Guillermo, Jorge EnriqueEchegaray Castillo, William C.Berrospi Zapana, Martin E.Linear systemsMarkov chainLyapunov equation and stabilitySistemas linealescadena de Markovecuación de Lyapunov y estabilidadIn this paper analyzed the stability of linear systems with continuous Markovian jumps. Firstly, the conditions for the Markov chain to be homogeneous and the state space is finite are imposed. Then the types of stability are presented, for example quadratic average stability, stochastic stability, exponential stability and almost certain stability. Stability in quadratic mean is analyzed by the real part of the eigenvalues of a certain matrix. Finally, an equation of Lyapunov is presented.En este trabajo analizaremos la estabilidad de los sistemas lineales con saltos markovianos en tiempo continuo. En primer lugar, se impone que la cadena de Markov sea homogénea y el espacio de estado sea finito.Luego se presentan los tipos de estabilidad, por ejemplo, estabilidad cuadrática promedio, estabilidad estocástica, estabilidad exponencial. La estabilidad en la media cuadrática se analiza mediante la parte real de los autovalores de una cierta matriz. Finalmente, se presenta una ecuación del tipo Lyapunov.National University of Trujillo - Academic Department of Mathematics2020-07-25info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArtículo evaluado por paresPeer-Review articleapplication/pdftext/htmlhttps://revistas.unitru.edu.pe/index.php/SSMM/article/view/2973Selecciones Matemáticas; Vol. 7 No. 01 (2020): January - July; 183-191Selecciones Matemáticas; Vol. 7 Núm. 01 (2020): Enero-Julio; 183-191Selecciones Matemáticas; v. 7 n. 01 (2020): Enero-Julio; 183-1912411-1783reponame:Revistas - Universidad Nacional de Trujilloinstname:Universidad Nacional de Trujilloinstacron:UNITRUspahttps://revistas.unitru.edu.pe/index.php/SSMM/article/view/2973/3300https://revistas.unitru.edu.pe/index.php/SSMM/article/view/2973/3813Derechos de autor 2020 Selecciones Matemáticasinfo:eu-repo/semantics/openAccessoai:ojs.revistas.unitru.edu.pe:article/29732022-10-21T18:51:17Z
dc.title.none.fl_str_mv Analysis of the stability of linear systems with continuous Markovian jumps
Análisis de la estabilidad de los sistemas lineales con saltos markovianos en tiempo continuo
title Analysis of the stability of linear systems with continuous Markovian jumps
spellingShingle Analysis of the stability of linear systems with continuous Markovian jumps
Mayta Guillermo, Jorge Enrique
Linear systems
Markov chain
Lyapunov equation and stability
Sistemas lineales
cadena de Markov
ecuación de Lyapunov y estabilidad
title_short Analysis of the stability of linear systems with continuous Markovian jumps
title_full Analysis of the stability of linear systems with continuous Markovian jumps
title_fullStr Analysis of the stability of linear systems with continuous Markovian jumps
title_full_unstemmed Analysis of the stability of linear systems with continuous Markovian jumps
title_sort Analysis of the stability of linear systems with continuous Markovian jumps
dc.creator.none.fl_str_mv Mayta Guillermo, Jorge Enrique
Echegaray Castillo, William C.
Berrospi Zapana, Martin E.
author Mayta Guillermo, Jorge Enrique
author_facet Mayta Guillermo, Jorge Enrique
Echegaray Castillo, William C.
Berrospi Zapana, Martin E.
author_role author
author2 Echegaray Castillo, William C.
Berrospi Zapana, Martin E.
author2_role author
author
dc.subject.none.fl_str_mv Linear systems
Markov chain
Lyapunov equation and stability
Sistemas lineales
cadena de Markov
ecuación de Lyapunov y estabilidad
topic Linear systems
Markov chain
Lyapunov equation and stability
Sistemas lineales
cadena de Markov
ecuación de Lyapunov y estabilidad
description In this paper analyzed the stability of linear systems with continuous Markovian jumps. Firstly, the conditions for the Markov chain to be homogeneous and the state space is finite are imposed. Then the types of stability are presented, for example quadratic average stability, stochastic stability, exponential stability and almost certain stability. Stability in quadratic mean is analyzed by the real part of the eigenvalues of a certain matrix. Finally, an equation of Lyapunov is presented.
publishDate 2020
dc.date.none.fl_str_mv 2020-07-25
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Artículo evaluado por pares
Peer-Review article
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://revistas.unitru.edu.pe/index.php/SSMM/article/view/2973
url https://revistas.unitru.edu.pe/index.php/SSMM/article/view/2973
dc.language.none.fl_str_mv spa
language spa
dc.relation.none.fl_str_mv https://revistas.unitru.edu.pe/index.php/SSMM/article/view/2973/3300
https://revistas.unitru.edu.pe/index.php/SSMM/article/view/2973/3813
dc.rights.none.fl_str_mv Derechos de autor 2020 Selecciones Matemáticas
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Derechos de autor 2020 Selecciones Matemáticas
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
text/html
dc.publisher.none.fl_str_mv National University of Trujillo - Academic Department of Mathematics
publisher.none.fl_str_mv National University of Trujillo - Academic Department of Mathematics
dc.source.none.fl_str_mv Selecciones Matemáticas; Vol. 7 No. 01 (2020): January - July; 183-191
Selecciones Matemáticas; Vol. 7 Núm. 01 (2020): Enero-Julio; 183-191
Selecciones Matemáticas; v. 7 n. 01 (2020): Enero-Julio; 183-191
2411-1783
reponame:Revistas - Universidad Nacional de Trujillo
instname:Universidad Nacional de Trujillo
instacron:UNITRU
instname_str Universidad Nacional de Trujillo
instacron_str UNITRU
institution UNITRU
reponame_str Revistas - Universidad Nacional de Trujillo
collection Revistas - Universidad Nacional de Trujillo
repository.name.fl_str_mv
repository.mail.fl_str_mv
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Analysis of the stability of linear systems with continuous Markovian jumps
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