A Local Parametrization of the State-Feedback Matrices in the Pole Assignment Problem
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915636672724992 |
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| author | Baragaña, I. Puerta, F. Zaballa, I. |
| author_facet | Baragaña, I. Puerta, F. Zaballa, I. |
| contents | Given a controllable system $(F,G)$, a local parametrization is obtained for the set of feedback gain matrices $K$ such that the state matrix, $F+GK$, of the closed loop system is in a prescribed similarity class. It is shown that this set can be endowed with the structure of a differentiable manifold whose dimension is also computed. Then a local parametrization and a local system of coordinates is provided using a diffeomorphism between this set of state feedback matrices and the orbit space of a set of truncated observability matrices via de action of a Lie group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20029 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Local Parametrization of the State-Feedback Matrices in the Pole Assignment Problem Baragaña, I. Puerta, F. Zaballa, I. Optimization and Control 93B27, 93B55, 93C05 Given a controllable system $(F,G)$, a local parametrization is obtained for the set of feedback gain matrices $K$ such that the state matrix, $F+GK$, of the closed loop system is in a prescribed similarity class. It is shown that this set can be endowed with the structure of a differentiable manifold whose dimension is also computed. Then a local parametrization and a local system of coordinates is provided using a diffeomorphism between this set of state feedback matrices and the orbit space of a set of truncated observability matrices via de action of a Lie group. |
| title | A Local Parametrization of the State-Feedback Matrices in the Pole Assignment Problem |
| topic | Optimization and Control 93B27, 93B55, 93C05 |
| url | https://arxiv.org/abs/2511.20029 |