On the regulator problem for linear systems over rings and algebras

The regulator problem is solvable for a linear dynamical system Σ\Sigma if and only if Σ\Sigma is both pole assignable and state estimable. In this case, Σ\Sigma is a canonical system (i.e., reachable and observable). When the ring RR is a field or a Noetherian total ring of fractions the convers...

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Autores principales:	Hermida-Alonso José Ángel, Carriegos Miguel V., Sáez-Schwedt Andrés, Sánchez-Giralda Tomás
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	linear systems over commutative rings regulator problem duality principle pole assignment 13p25 93b25 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/5b7ccb2f50494b9ba7f129c40bc4d0db
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spelling	oai:doaj.org-article:5b7ccb2f50494b9ba7f129c40bc4d0db2021-12-05T14:10:52ZOn the regulator problem for linear systems over rings and algebras2391-545510.1515/math-2021-0002https://doaj.org/article/5b7ccb2f50494b9ba7f129c40bc4d0db2021-04-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0002https://doaj.org/toc/2391-5455The regulator problem is solvable for a linear dynamical system Σ\Sigma if and only if Σ\Sigma is both pole assignable and state estimable. In this case, Σ\Sigma is a canonical system (i.e., reachable and observable). When the ring RR is a field or a Noetherian total ring of fractions the converse is true. Commutative rings which have the property that the regulator problem is solvable for every canonical system (RP-rings) are characterized as the class of rings where every observable system is state estimable (SE-rings), and this class is shown to be equal to the class of rings where every reachable system is pole-assignable (PA-rings) and the dual of a canonical system is also canonical (DP-rings).Hermida-Alonso José ÁngelCarriegos Miguel V.Sáez-Schwedt AndrésSánchez-Giralda TomásDe Gruyterarticlelinear systems over commutative ringsregulator problemduality principlepole assignment13p2593b25MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 101-110 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	linear systems over commutative rings regulator problem duality principle pole assignment 13p25 93b25 Mathematics QA1-939
spellingShingle	linear systems over commutative rings regulator problem duality principle pole assignment 13p25 93b25 Mathematics QA1-939 Hermida-Alonso José Ángel Carriegos Miguel V. Sáez-Schwedt Andrés Sánchez-Giralda Tomás On the regulator problem for linear systems over rings and algebras
description	The regulator problem is solvable for a linear dynamical system Σ\Sigma if and only if Σ\Sigma is both pole assignable and state estimable. In this case, Σ\Sigma is a canonical system (i.e., reachable and observable). When the ring RR is a field or a Noetherian total ring of fractions the converse is true. Commutative rings which have the property that the regulator problem is solvable for every canonical system (RP-rings) are characterized as the class of rings where every observable system is state estimable (SE-rings), and this class is shown to be equal to the class of rings where every reachable system is pole-assignable (PA-rings) and the dual of a canonical system is also canonical (DP-rings).
format	article
author	Hermida-Alonso José Ángel Carriegos Miguel V. Sáez-Schwedt Andrés Sánchez-Giralda Tomás
author_facet	Hermida-Alonso José Ángel Carriegos Miguel V. Sáez-Schwedt Andrés Sánchez-Giralda Tomás
author_sort	Hermida-Alonso José Ángel
title	On the regulator problem for linear systems over rings and algebras
title_short	On the regulator problem for linear systems over rings and algebras
title_full	On the regulator problem for linear systems over rings and algebras
title_fullStr	On the regulator problem for linear systems over rings and algebras
title_full_unstemmed	On the regulator problem for linear systems over rings and algebras
title_sort	on the regulator problem for linear systems over rings and algebras
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/5b7ccb2f50494b9ba7f129c40bc4d0db
work_keys_str_mv	AT hermidaalonsojoseangel ontheregulatorproblemforlinearsystemsoverringsandalgebras AT carriegosmiguelv ontheregulatorproblemforlinearsystemsoverringsandalgebras AT saezschwedtandres ontheregulatorproblemforlinearsystemsoverringsandalgebras AT sanchezgiraldatomas ontheregulatorproblemforlinearsystemsoverringsandalgebras
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On the regulator problem for linear systems over rings and algebras

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