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RECERCAT Home > Universitat Politècnica de Catalunya > Documents de recerca > View document

To access the full text documents, please follow this link: http://hdl.handle.net/2117/904

Title:	On the geometry of the solutions of the cover problem
Author:	Puerta Sales, Ferran; Puerta Coll, Xavier; Zaballa, Ion
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
Abstract:	For a given system (A;B) and a subspace S, the Cover Problem consits of ¯nding all (A;B)-invariant subspacescontaining S. For controllable systems, the set of these subspaces can be suitably strati¯ed. In this paper, necessary andsu±cient conditions are given for the cover problem to have a solution on a given strata. Then the geometry of these solutionsis studied. In particular, the set of the solutions is provided with a di®erentiable structure and a parametrization of all solutionsis obtained through a coordinate atlas of the corresponding smooth manifold.
Publication date:	2012-05-10
Subject(s):	System theory Algebras, Linear Multilinear algebra Matrices Cover problem controlled invariant subspace smooth manifold coordinate chart Brunovsky indices Sistemes, Teoria de Àlgebra lineal Àlgebra multilineal Matriu S, Teoria /Classificació AMS/93 Systems Theory; Control/93B Controllability, observability, and system structure /Classificació AMS/15 Linear and multilinear algebra; matrix theory
Rights:	Consulteu les condicions d'ús d'aquest document en el repositori original:http://hdl.handle.net/2117/904
Document type:	Article
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