On the geometry of the solutions of the cover problem
For a given system (A;B) and a subspace S, the Cover Problem consits of ¯nding all (A;B)-invariant subspaces containing S. For controllable systems, the set of these subspaces can be suitably strati¯ed. In this paper, necessary and su±cient conditions are given for the cover problem to have a soluti...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2003 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/904 |
| Acceso en línea: | https://hdl.handle.net/2117/904 |
| Access Level: | acceso abierto |
| Palabra clave: | System theory Algebras, Linear Multilinear algebra Matrices Cover problem controlled invariant subspace smooth manifold coordinate chart Brunovsky indices Sistemes, Teoria de Àlgebra lineal Àlgebra multilineal Matriu S, Teoria Classificació AMS::93 Systems Theory Control::93B Controllability, observability, and system structure Classificació AMS::15 Linear and multilinear algebra matrix theory |
| Sumario: | For a given system (A;B) and a subspace S, the Cover Problem consits of ¯nding all (A;B)-invariant subspaces containing S. For controllable systems, the set of these subspaces can be suitably strati¯ed. In this paper, necessary and su±cient conditions are given for the cover problem to have a solution on a given strata. Then the geometry of these solutions is studied. In particular, the set of the solutions is provided with a di®erentiable structure and a parametrization of all solutions is obtained through a coordinate atlas of the corresponding smooth manifold. |
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