On the Geometry of the Solutions of the Cover Problem

For a given system $\Sigma(A,B)$ and a subspace $\maths$, the cover problem consists of finding all $(A,B)$-invariant subspaces containing $\maths$. For controllable systems, the set of these subspaces can be suitably stratified. In this paper, necessary and sufficient conditions are given for the c...

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Bibliographic Details
Published inSIAM journal on control and optimization Vol. 45; no. 2; pp. 389 - 413
Main Authors Puerta, F., Puerta, X., Zaballa, I.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2006
Subjects
Geometry
System theory
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Summary:For a given system $\Sigma(A,B)$ and a subspace $\maths$, the cover problem consists of finding all $(A,B)$-invariant subspaces containing $\maths$. For controllable systems, the set of these subspaces can be suitably stratified. In this paper, necessary and sufficient 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 differentiable structure and a parameterization of all solutions is obtained through a coordinate atlas of the corresponding smooth manifold.
ISSN:0363-0129
1095-7138
DOI:10.1137/S0363012904443087