Reconstructibility of time-invariant and periodic behavioural systems
Autor(a) principal: | |
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Data de Publicação: | 2013 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | https://hdl.handle.net/10216/110100 |
Resumo: | In this article, the properties of behavioural reconstructibility and forward-observability for systems over the whole time axis Z are introduced. These properties are characterised in terms of appropriate rank conditions, for the time-invariant case. A comparison is made with the existing results in the behavioural setting as well as in the classical state space framework. In the particular case of a periodic system, it is shown that there exists an equivalence between the reconstructibility of the periodic system and its associated lifted system, which is time-invariant. Furthermore, we prove that, for a classical state space system, state reconstructibility is equivalent to behavioural reconstructibility, regardless of the time varying or time-invariant nature of the system. This allows deriving rank tests for the cases of time-invariant and of periodic systems, rediscovering the already known results for state reconstructibility from an alternative perspective. The obtained results contribute to establishing links between two different settings, thus providing a better insight into the considered systems properties. |
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Reconstructibility of time-invariant and periodic behavioural systemsEngenharia electrotécnica, electrónica e informáticaElectrical engineering, Electronic engineering, Information engineeringIn this article, the properties of behavioural reconstructibility and forward-observability for systems over the whole time axis Z are introduced. These properties are characterised in terms of appropriate rank conditions, for the time-invariant case. A comparison is made with the existing results in the behavioural setting as well as in the classical state space framework. In the particular case of a periodic system, it is shown that there exists an equivalence between the reconstructibility of the periodic system and its associated lifted system, which is time-invariant. Furthermore, we prove that, for a classical state space system, state reconstructibility is equivalent to behavioural reconstructibility, regardless of the time varying or time-invariant nature of the system. This allows deriving rank tests for the cases of time-invariant and of periodic systems, rediscovering the already known results for state reconstructibility from an alternative perspective. The obtained results contribute to establishing links between two different settings, thus providing a better insight into the considered systems properties.20132013-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10216/110100eng0020-717910.1080/00207179.2012.719636Aleixo, JCRocha, Pinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-29T12:56:47Zoai:repositorio-aberto.up.pt:10216/110100Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T23:30:09.530648Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Reconstructibility of time-invariant and periodic behavioural systems |
title |
Reconstructibility of time-invariant and periodic behavioural systems |
spellingShingle |
Reconstructibility of time-invariant and periodic behavioural systems Aleixo, JC Engenharia electrotécnica, electrónica e informática Electrical engineering, Electronic engineering, Information engineering |
title_short |
Reconstructibility of time-invariant and periodic behavioural systems |
title_full |
Reconstructibility of time-invariant and periodic behavioural systems |
title_fullStr |
Reconstructibility of time-invariant and periodic behavioural systems |
title_full_unstemmed |
Reconstructibility of time-invariant and periodic behavioural systems |
title_sort |
Reconstructibility of time-invariant and periodic behavioural systems |
author |
Aleixo, JC |
author_facet |
Aleixo, JC Rocha, P |
author_role |
author |
author2 |
Rocha, P |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Aleixo, JC Rocha, P |
dc.subject.por.fl_str_mv |
Engenharia electrotécnica, electrónica e informática Electrical engineering, Electronic engineering, Information engineering |
topic |
Engenharia electrotécnica, electrónica e informática Electrical engineering, Electronic engineering, Information engineering |
description |
In this article, the properties of behavioural reconstructibility and forward-observability for systems over the whole time axis Z are introduced. These properties are characterised in terms of appropriate rank conditions, for the time-invariant case. A comparison is made with the existing results in the behavioural setting as well as in the classical state space framework. In the particular case of a periodic system, it is shown that there exists an equivalence between the reconstructibility of the periodic system and its associated lifted system, which is time-invariant. Furthermore, we prove that, for a classical state space system, state reconstructibility is equivalent to behavioural reconstructibility, regardless of the time varying or time-invariant nature of the system. This allows deriving rank tests for the cases of time-invariant and of periodic systems, rediscovering the already known results for state reconstructibility from an alternative perspective. The obtained results contribute to establishing links between two different settings, thus providing a better insight into the considered systems properties. |
publishDate |
2013 |
dc.date.none.fl_str_mv |
2013 2013-01-01T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://hdl.handle.net/10216/110100 |
url |
https://hdl.handle.net/10216/110100 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0020-7179 10.1080/00207179.2012.719636 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
|
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1799135609180127232 |