On the Equivalence between Integer-and Fractional Order-Models of Continuous-Time and Discrete-Time ARMA Systems

Detalhes bibliográficos
Autor(a) principal: Ortigueira, Manuel Duarte
Data de Publicação: 2022
Outros Autores: Magin, Richard L.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/143502
Resumo: Publisher Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland.
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spelling On the Equivalence between Integer-and Fractional Order-Models of Continuous-Time and Discrete-Time ARMA Systemsautoregressive-moving averagebilinear discrete-time systemscontinuous-time ARMAdiscrete-time ARMAembeddingequivalenceFARMAfractional ARMAidentificationAnalysisStatistical and Nonlinear PhysicsStatistics and ProbabilityPublisher Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland.The equivalence of continuous-/discrete-time autoregressive-moving average (ARMA) systems is considered in this paper. For the integer-order cases, the interrelations between systems defined by continuous-time (CT) differential and discrete-time (DT) difference equations are found, leading to formulae relating partial fractions of the continuous and discrete transfer functions. Simple transformations are presented to allow interconversions between both systems, recovering formulae obtained with the impulse invariant method. These transformations are also used to formulate a covariance equivalence. The spectral correspondence implied by the bilinear (Tustin) transformation is used to study the equivalence between the two types of systems. The general fractional CT/DT ARMA systems are also studied by considering two DT differential fractional autoregressive-moving average (FARMA) systems based on the nabla/delta and bilinear derivatives. The interrelations CT/DT are also considered, paying special attention to the systems defined by the bilinear derivatives.CTS - Centro de Tecnologia e SistemasDEE2010-B2 SistemasUNINOVA-Instituto de Desenvolvimento de Novas TecnologiasDEE - Departamento de Engenharia Electrotécnica e de ComputadoresRUNOrtigueira, Manuel DuarteMagin, Richard L.2022-09-05T22:25:51Z2022-04-282022-04-28T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article34application/pdfhttp://hdl.handle.net/10362/143502eng2504-3110PURE: 46297490https://doi.org/10.3390/fractalfract6050242info: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:RCAAP2024-03-11T05:21:52Zoai:run.unl.pt:10362/143502Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:50:58.412943Repositório 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 On the Equivalence between Integer-and Fractional Order-Models of Continuous-Time and Discrete-Time ARMA Systems
title On the Equivalence between Integer-and Fractional Order-Models of Continuous-Time and Discrete-Time ARMA Systems
spellingShingle On the Equivalence between Integer-and Fractional Order-Models of Continuous-Time and Discrete-Time ARMA Systems
Ortigueira, Manuel Duarte
autoregressive-moving average
bilinear discrete-time systems
continuous-time ARMA
discrete-time ARMA
embedding
equivalence
FARMA
fractional ARMA
identification
Analysis
Statistical and Nonlinear Physics
Statistics and Probability
title_short On the Equivalence between Integer-and Fractional Order-Models of Continuous-Time and Discrete-Time ARMA Systems
title_full On the Equivalence between Integer-and Fractional Order-Models of Continuous-Time and Discrete-Time ARMA Systems
title_fullStr On the Equivalence between Integer-and Fractional Order-Models of Continuous-Time and Discrete-Time ARMA Systems
title_full_unstemmed On the Equivalence between Integer-and Fractional Order-Models of Continuous-Time and Discrete-Time ARMA Systems
title_sort On the Equivalence between Integer-and Fractional Order-Models of Continuous-Time and Discrete-Time ARMA Systems
author Ortigueira, Manuel Duarte
author_facet Ortigueira, Manuel Duarte
Magin, Richard L.
author_role author
author2 Magin, Richard L.
author2_role author
dc.contributor.none.fl_str_mv CTS - Centro de Tecnologia e Sistemas
DEE2010-B2 Sistemas
UNINOVA-Instituto de Desenvolvimento de Novas Tecnologias
DEE - Departamento de Engenharia Electrotécnica e de Computadores
RUN
dc.contributor.author.fl_str_mv Ortigueira, Manuel Duarte
Magin, Richard L.
dc.subject.por.fl_str_mv autoregressive-moving average
bilinear discrete-time systems
continuous-time ARMA
discrete-time ARMA
embedding
equivalence
FARMA
fractional ARMA
identification
Analysis
Statistical and Nonlinear Physics
Statistics and Probability
topic autoregressive-moving average
bilinear discrete-time systems
continuous-time ARMA
discrete-time ARMA
embedding
equivalence
FARMA
fractional ARMA
identification
Analysis
Statistical and Nonlinear Physics
Statistics and Probability
description Publisher Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland.
publishDate 2022
dc.date.none.fl_str_mv 2022-09-05T22:25:51Z
2022-04-28
2022-04-28T00:00:00Z
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 http://hdl.handle.net/10362/143502
url http://hdl.handle.net/10362/143502
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 2504-3110
PURE: 46297490
https://doi.org/10.3390/fractalfract6050242
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 34
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
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