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Título
On the regulator problem for linear systems over rings and algebras
Autor
Facultad/Centro
Área de conocimiento
Título de la revista
Open Mathematics
Número de la revista
1
Cita Bibliográfica
Hermida-Alonso, J. Á., Carriegos, M. V., Sáez-Schwedt, A., & Sánchez-Giralda, T. (2021). On the regulator problem for linear systems over rings and algebras. Open Mathematics, 19(1), 101-110. https://doi.org/10.1515/MATH-2021-0002
Editorial
De Gruyter
Fecha
2021
Resumen
[EN] The regulator problem is solvable for a linear dynamical system
Σ
if and only if
Σ
is both pole assignable and state estimable. In this case,
Σ
is a canonical system (i.e., reachable and observable). When the ring
R
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).
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