Asymptotic Hyperstability and Input–Output Energy Positivity of a Single-Input Single-Output System Which Incorporates a Memoryless Non-Linear Device in the Feed-Forward Loop

This paper visualizes the role of hyperstable controllers in the closed-loop asymptotic stability of a single-input single-output system subject to any nonlinear and eventually time-varying controller within the hyperstable class. The feed-forward controlled loop (or controlled plant) contains a str...

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Autor: De la Sen Parte, Manuel
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universidad del País Vasco
Repositorio:Addi. Archivo Digital para la Docencia y la Investigación
OAI Identifier:oai:addi.ehu.eus:10810/57181
Acceso en línea:http://hdl.handle.net/10810/57181
Access Level:acceso abierto
Palabra clave:positive realness
hyperstability
asymptotic hyperstability
passivity
sample and hold devices
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spelling Asymptotic Hyperstability and Input–Output Energy Positivity of a Single-Input Single-Output System Which Incorporates a Memoryless Non-Linear Device in the Feed-Forward LoopDe la Sen Parte, Manuelpositive realnesshyperstabilityasymptotic hyperstabilitypassivitysample and hold devicesThis paper visualizes the role of hyperstable controllers in the closed-loop asymptotic stability of a single-input single-output system subject to any nonlinear and eventually time-varying controller within the hyperstable class. The feed-forward controlled loop (or controlled plant) contains a strongly strictly positive real transfer function in parallel with a non-linear and memory-free device. The properties of positivity and boundedness of the input–output energy are examined based on the “ad hoc” use of the Rayleigh energy theorem on the truncated relevant signals for finite time intervals. The cases of minimal and non-minimal state-space realizations of the linear part are characterized from a global asymptotic stability (asymptotic hyperstability) point of view. Some related extended results are obtained for the case when the linear part is both positive real and externally positive and for the case of incorporation of other linear components which are stable but not necessarily positive real.This research was funded by the Spanish Government and the European Commission, grant number RTI2018-094336-B-I00 (MCIU/AEI/FEDER, UE) and by the Basque Government, grant number IT1207-19. The APC was funded by grant RTI2018-094336-B-I00 (MCIU/AEI/FEDER, UE).MDPI2022202220222022info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10810/57181reponame:Addi. Archivo Digital para la Docencia y la Investigacióninstname:Universidad del País VascoInglésinfo:eu-repo/grantAgreement/MICIU/RTI2018-094336-B-I0/https://www.mdpi.com/2227-7390/10/12/2051info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/© 2022 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).oai:addi.ehu.eus:10810/571812026-06-18T09:23:17Z
dc.title.none.fl_str_mv Asymptotic Hyperstability and Input–Output Energy Positivity of a Single-Input Single-Output System Which Incorporates a Memoryless Non-Linear Device in the Feed-Forward Loop
title Asymptotic Hyperstability and Input–Output Energy Positivity of a Single-Input Single-Output System Which Incorporates a Memoryless Non-Linear Device in the Feed-Forward Loop
spellingShingle Asymptotic Hyperstability and Input–Output Energy Positivity of a Single-Input Single-Output System Which Incorporates a Memoryless Non-Linear Device in the Feed-Forward Loop
De la Sen Parte, Manuel
positive realness
hyperstability
asymptotic hyperstability
passivity
sample and hold devices
title_short Asymptotic Hyperstability and Input–Output Energy Positivity of a Single-Input Single-Output System Which Incorporates a Memoryless Non-Linear Device in the Feed-Forward Loop
title_full Asymptotic Hyperstability and Input–Output Energy Positivity of a Single-Input Single-Output System Which Incorporates a Memoryless Non-Linear Device in the Feed-Forward Loop
title_fullStr Asymptotic Hyperstability and Input–Output Energy Positivity of a Single-Input Single-Output System Which Incorporates a Memoryless Non-Linear Device in the Feed-Forward Loop
title_full_unstemmed Asymptotic Hyperstability and Input–Output Energy Positivity of a Single-Input Single-Output System Which Incorporates a Memoryless Non-Linear Device in the Feed-Forward Loop
title_sort Asymptotic Hyperstability and Input–Output Energy Positivity of a Single-Input Single-Output System Which Incorporates a Memoryless Non-Linear Device in the Feed-Forward Loop
dc.creator.none.fl_str_mv De la Sen Parte, Manuel
author De la Sen Parte, Manuel
author_facet De la Sen Parte, Manuel
author_role author
dc.subject.none.fl_str_mv positive realness
hyperstability
asymptotic hyperstability
passivity
sample and hold devices
topic positive realness
hyperstability
asymptotic hyperstability
passivity
sample and hold devices
description This paper visualizes the role of hyperstable controllers in the closed-loop asymptotic stability of a single-input single-output system subject to any nonlinear and eventually time-varying controller within the hyperstable class. The feed-forward controlled loop (or controlled plant) contains a strongly strictly positive real transfer function in parallel with a non-linear and memory-free device. The properties of positivity and boundedness of the input–output energy are examined based on the “ad hoc” use of the Rayleigh energy theorem on the truncated relevant signals for finite time intervals. The cases of minimal and non-minimal state-space realizations of the linear part are characterized from a global asymptotic stability (asymptotic hyperstability) point of view. Some related extended results are obtained for the case when the linear part is both positive real and externally positive and for the case of incorporation of other linear components which are stable but not necessarily positive real.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022
2022
2022
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10810/57181
url http://hdl.handle.net/10810/57181
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/MICIU/RTI2018-094336-B-I0/
https://www.mdpi.com/2227-7390/10/12/2051
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/4.0/
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv MDPI
publisher.none.fl_str_mv MDPI
dc.source.none.fl_str_mv reponame:Addi. Archivo Digital para la Docencia y la Investigación
instname:Universidad del País Vasco
instname_str Universidad del País Vasco
reponame_str Addi. Archivo Digital para la Docencia y la Investigación
collection Addi. Archivo Digital para la Docencia y la Investigación
repository.name.fl_str_mv
repository.mail.fl_str_mv
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