{"ID":2836808,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.20029","arxiv_id":"2511.20029","title":"A Local Parametrization of the State-Feedback Matrices in the Pole Assignment Problem","abstract":"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.","short_abstract":"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 i...","url_abs":"https://arxiv.org/abs/2511.20029","url_pdf":"https://arxiv.org/pdf/2511.20029v1","authors":"[\"I. Baragaña\",\"F. Puerta\",\"I. Zaballa\"]","published":"2025-11-25T07:54:11Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}