On the regulator problem for linear systems over rings and algebras
[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. Commut...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universidad Rey Juan Carlos |
| Repositorio: | BULERIA. Repositorio Institucional de la Universidad de León |
| OAI Identifier: | oai:buleria.unileon.es:10612/19427 |
| Acceso en línea: | https://www.degruyter.com/document/doi/10.1515/math-2021-0002/html https://hdl.handle.net/10612/19427 |
| Access Level: | acceso abierto |
| Palabra clave: | Matemáticas Linear systems over commutative rings Regulator problem Duality principle Pole assignment 1201.05 Campos, Anillos, Álgebras 1201.10 Álgebra Lineal |
| Sumario: | [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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