The topology of the set of conditioned invariant subspaces
We consider the topology of the set of conditioned invariant subspaces of an observable pair $(C,A)$ of a fixed dimension. By fixing the observability indices of the restricted system, a stratification by finitely many smooth manifolds is obtained, termed Brunovsky strata. It is shown that each Brun...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 1999 |
| 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:2117/777 |
| Acceso en línea: | https://hdl.handle.net/2117/777 |
| Access Level: | acceso abierto |
| Palabra clave: | System theory Global analysis (Mathematics) Topology Invariant subspaces Sistemes, Teoria de Sistemes de control Varietats (Matemàtica) Classificació AMS::93 Systems Theory Control::93B Controllability, observability, and system structure Classificació AMS::58 Global analysis, analysis on manifolds::58E Variational problems in infinite-dimensional spaces Control::93C Control systems, guided systems |
| Sumario: | We consider the topology of the set of conditioned invariant subspaces of an observable pair $(C,A)$ of a fixed dimension. By fixing the observability indices of the restricted system, a stratification by finitely many smooth manifolds is obtained, termed Brunovsky strata. It is shown that each Brunovsky stratum is homotopy equivalent to a generalized flag manifold. From this description an effective formula for the Betti numbers of the Brunovsky strata can be derived. |
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