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Stratification and bundle structure of the set of conditioned invariant subspaces in the general case
Ferrer Llop, Josep; Puerta Sales, Ferran; Puerta Coll, Xavier
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
We extend some known results about the smooth stratification of the set of conditioned invariant subspaces for a general pair $(C,A)\in\w C^n\times\w C^{n+m}$ without any assumption on the observability. More precisely we prove that the set of $(C,A)$-conditioned invariant subspaces having a fixed Brunovsky-Kronecker structure is a submanifold of the corresponding Grassman manifold, with a vector bundle structure relating the observable and nonobservable part, and we compute its dimension. We also prove that the set of all $(C,A)$-conditioned invariant subspaces having a fixed dimension is connected, provided that the nonobservable part of $(C,A)$ has at most one eigenvalue (this condition is in general necessary).
System theory
conditioned invariant subspace
Brunovsky bases
orbit space
fiber bundle
Grassmann manifold
Sistemes, Teoria de
Sistemes de control
Classificació AMS::93 Systems Theory; Control::93B Controllability, observability, and system structure
Classificació AMS::93 Systems Theory; Control::93C Control systems, guided systems
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
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