Stratification and bundle structure of the set of conditioned invariant subspaces in the general case

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Document typeArticle
Defense date2003
Rights accessOpen Access
Abstract
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).
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