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...

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Detalles Bibliográficos
Autores: Puerta Coll, Xavier, Helmke, Uwe
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
Descripción
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.