Orbits of controllable and observable systems

Let a time-invariant linear system $\left .\aligned \dot x(t)&=Ax(t)+Bu(t)\\y(t)&=Cx(t)\endaligned \right \}$ corresponding to a realization of a prescribed transfer function matrix can be represented by triples of matrices $(A,B,C)$. The permitted transformations of basis changes in the spa...

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Detalles Bibliográficos
Autores: Clotet Juan, Josep|||0000-0002-9550-728X, García Planas, María Isabel|||0000-0001-7418-7208
Tipo de recurso: artículo
Fecha de publicación:1999
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/1049
Acceso en línea:https://hdl.handle.net/2117/1049
Access Level:acceso abierto
Palabra clave:System theory
Algebras, Linear
Multilinear algebra
Matrices
Controllability
Observability
Lie group action
Orbits
Sistemes, Teoria de
Àlgebra lineal
Àlgebra multilineal
Matriu S, Teoria
Classificació AMS::15 Linear and multilinear algebra
matrix theory
Classificació AMS::93 Systems Theory
Control::93B Controllability, observability, and system structure
id ES_6c1eea8543b4e191fdae664c219d488b
oai_identifier_str oai:upcommons.upc.edu:2117/1049
network_acronym_str ES
network_name_str España
repository_id_str
spelling Orbits of controllable and observable systemsClotet Juan, Josep|||0000-0002-9550-728XGarcía Planas, María Isabel|||0000-0001-7418-7208System theoryAlgebras, LinearMultilinear algebraMatricesControllabilityObservabilityLie group actionOrbitsSistemes, Teoria deÀlgebra linealÀlgebra multilinealMatriu S, TeoriaClassificació AMS::15 Linear and multilinear algebramatrix theoryClassificació AMS::93 Systems TheoryControl::93B Controllability, observability, and system structureLet a time-invariant linear system $\left .\aligned \dot x(t)&=Ax(t)+Bu(t)\\y(t)&=Cx(t)\endaligned \right \}$ corresponding to a realization of a prescribed transfer function matrix can be represented by triples of matrices $(A,B,C)$. The permitted transformations of basis changes in the space state on the systems can be seen in the space of triples of matrices as similarity equivalence. In this paper we give a geometric characteriaztion of controllable and observable systems as orbits under a Lie group action. As a corollary we obtain a lower bound of the distance between a controllable and observable triple and the nearest uncontrollable one.19991999-01-0120072007-05-28journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/1049reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 2.5 Spainhttp://creativecommons.org/licenses/by-nc-nd/2.5/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/10492026-05-27T15:37:01Z
dc.title.none.fl_str_mv Orbits of controllable and observable systems
title Orbits of controllable and observable systems
spellingShingle Orbits of controllable and observable systems
Clotet Juan, Josep|||0000-0002-9550-728X
System theory
Algebras, Linear
Multilinear algebra
Matrices
Controllability
Observability
Lie group action
Orbits
Sistemes, Teoria de
Àlgebra lineal
Àlgebra multilineal
Matriu S, Teoria
Classificació AMS::15 Linear and multilinear algebra
matrix theory
Classificació AMS::93 Systems Theory
Control::93B Controllability, observability, and system structure
title_short Orbits of controllable and observable systems
title_full Orbits of controllable and observable systems
title_fullStr Orbits of controllable and observable systems
title_full_unstemmed Orbits of controllable and observable systems
title_sort Orbits of controllable and observable systems
dc.creator.none.fl_str_mv Clotet Juan, Josep|||0000-0002-9550-728X
García Planas, María Isabel|||0000-0001-7418-7208
author Clotet Juan, Josep|||0000-0002-9550-728X
author_facet Clotet Juan, Josep|||0000-0002-9550-728X
García Planas, María Isabel|||0000-0001-7418-7208
author_role author
author2 García Planas, María Isabel|||0000-0001-7418-7208
author2_role author
dc.subject.none.fl_str_mv System theory
Algebras, Linear
Multilinear algebra
Matrices
Controllability
Observability
Lie group action
Orbits
Sistemes, Teoria de
Àlgebra lineal
Àlgebra multilineal
Matriu S, Teoria
Classificació AMS::15 Linear and multilinear algebra
matrix theory
Classificació AMS::93 Systems Theory
Control::93B Controllability, observability, and system structure
topic System theory
Algebras, Linear
Multilinear algebra
Matrices
Controllability
Observability
Lie group action
Orbits
Sistemes, Teoria de
Àlgebra lineal
Àlgebra multilineal
Matriu S, Teoria
Classificació AMS::15 Linear and multilinear algebra
matrix theory
Classificació AMS::93 Systems Theory
Control::93B Controllability, observability, and system structure
description Let a time-invariant linear system $\left .\aligned \dot x(t)&=Ax(t)+Bu(t)\\y(t)&=Cx(t)\endaligned \right \}$ corresponding to a realization of a prescribed transfer function matrix can be represented by triples of matrices $(A,B,C)$. The permitted transformations of basis changes in the space state on the systems can be seen in the space of triples of matrices as similarity equivalence. In this paper we give a geometric characteriaztion of controllable and observable systems as orbits under a Lie group action. As a corollary we obtain a lower bound of the distance between a controllable and observable triple and the nearest uncontrollable one.
publishDate 1999
dc.date.none.fl_str_mv 1999
1999-01-01
2007
2007-05-28
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/1049
url https://hdl.handle.net/2117/1049
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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