Browsing by Author "Puerta Coll, Xavier"
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A cellular decomposition of the manifold of observable conditioned invariant subspaces
Puerta Sales, Ferran; Puerta Coll, Xavier; Zaballa, Ion (2000)
Article
Open AccessGiven an observable system defined by a pair of matrices $(C,A)$ we obtain a cellular decomposition of the manifold of $(C,A)$conditioned invariant subspaces having the restricted system fixed observability indices and ... 
A coordinate atlas of the manifold of observable conditioned invariant subspaces
Puerta Sales, Ferran; Puerta Coll, Xavier; Zaballa, I (200102)
Article
Open AccessGiven an observable system (C,A) € Km×n×Kn×n with K = R or C , the set of (C,A) invariant subspaces having the restricted system fixed observability indices is a smooth manifold embedded on the corresponding Grassmannian. ... 
A geometrical aprroach to C<sup>p</sup>globalization of pointwise matricial relations
Puerta Sales, Ferran; Puerta Coll, Xavier (1999)
External research report
Open Access 
A sufficient condition for Lipschitz stability of controlled Invariant subspaces
Peña Carrera, Marta; Puerta Sales, Ferran; Puerta Coll, Xavier (200912)
Article
Restricted access  publisher's policyGiven a pair of matrices (A,B) we study the Lipschitz stability of its controlled invariant subspaces. A sufficient condition is derived from the geometry of the set formed by the quadruples (A,B, F, S) where S is ... 
Classification and versal deformation of generalized flags
Puerta Coll, Xavier (2003)
Article
Open AccessA natural equivalence relation can be considered in the generalized flag manifold. First we give a complete set of invariants of it as well as a canonical matrix description of the classes. Next we consider parametric ... 
Global reduction to the Kronecker canonical form of a C^rfamily of timeinvariant linear systems
Ferrer Llop, Josep; Puerta Sales, Ferran; Puerta Coll, Xavier (1999)
Article
Open AccessWe present a geometric approach to the study of timeinvariant systems, represented by quadruples of matrices (A, B, C, D). Our main goal is, given a differentiable family of such quadruples having constant Kronecker type, ... 
MÈTODES MATEMÀTICS I (Examen 1r quadrimestre, 1r parcial)
Puerta Coll, Xavier (Universitat Politècnica de Catalunya, 20171106)
Exam
Restricted access to the UPC academic community 
MÈTODES MATEMÀTICS I (Examen 1r quadrimestre, 2n parcial)
Puerta Coll, Xavier (Universitat Politècnica de Catalunya, 20180110)
Exam
Restricted access to the UPC academic community 
MÈTODES MATEMÀTICS II (Examen 2n quadrimestre, 1r parcial)
Puerta Coll, Xavier (Universitat Politècnica de Catalunya, 20170407)
Exam
Restricted access to the UPC academic community 
MÈTODES MATEMÀTICS II (Examen 2n quadrimestre, 1r parcial)
Sabater Pruna, M. Assumpta; Puerta Coll, Xavier (Universitat Politècnica de Catalunya, 20180418)
Exam
Restricted access to the UPC academic community 
On the geometry of the generalized partial realization problem
Baragaña, Itziar; Puerta Sales, Ferran; Puerta Coll, Xavier; Zaballa, Ion (201009)
Article
Restricted access  publisher's policyThe geometry of the set of generalized partial realizations of a finite nice sequence of matrices is studied. It is proved that this set is a stratified manifold, the dimension of their strata is computed and its connection ... 
On the geometry of the solutions of the cover problem
Puerta Sales, Ferran; Puerta Coll, Xavier; Zaballa, Ion (2003)
Article
Open AccessFor a given system (A;B) and a subspace S, the Cover Problem consits of ¯nding all (A;B)invariant subspaces containing S. For controllable systems, the set of these subspaces can be suitably strati¯ed. In this paper, ... 
On the parametrization of the controllability pairs of a controllable subspaces of a controllable pair
Puerta Sales, Ferran; Puerta Coll, Xavier; Zaballa, Ion (2004)
Article
Open AccessGiven a controllable linear control system defined by a pair of constant matrices (A,B), the set of controllability subspaces is a stratified submanifold of the set of (A,B)invariant subspaces. We parametrize each strata ... 
On the parametrization of the controllability subspaces of a controllable pair
Puerta Sales, Ferran; Puerta Coll, Xavier; Zaballa, Ion (2003)
Article
Open AccessGiven a controllable linear control system defined by a pair of constant matrices (A;B), the set of controllability subspaces is an stratified submanifold of the set of (A;B)invariant subspaces. We parameterize each ... 
On the perturbation of bimodal systems
Puerta Coll, Xavier; Puerta Sales, Ferran (Servicio de publicaciones de la UPV, 2010)
Conference lecture
Open AccessGiven a bimodal system de¯ned by the equations ½ x_ (t) = A1x(t) + Bu(t) if ctx(t) · 0 x_ (t) = A2x(t) + Bu(t) if ctx(t) ¸ 0 (1) where B 2Mn;m and Ai 2Mn, i = 1; 2, are such that A1;A2 coincide on the hyper plane V ... 
On the stratifications of the set of $(A,B)$invariant and controllability subspaces
Puerta Sales, Ferran; Puerta Coll, Xavier (2001)
Article
Open Access 
Output Maximal Dimension for the Disturbance Decoupling Problem
Puerta Sales, Ferran; Puerta Coll, Xavier; Zaballa, Ion (2001)
Article
Open AccessGiven a linear time invariant system with a disturbance we describe a method of finding the maximal dimensional output for a generic Disturbance Decoupling problem. 
Perturbation of quadrics
Clotet Juan, Josep; Magret Planas, Maria dels Dolors; Puerta Coll, Xavier (2000)
Article
Open AccessThe aim of this paper is to study what happens when a slight perturbation affects the coefficients of a quadratic equation defining a variety (a quadric) in R^n. Structurally stable quadrics are those a small perturbation ... 
Simultaneous versal deformations of endomorphisms and invariant subspaces
Compta Creus, Albert; Helmke, Uwe; Peña Carrera, Marta; Puerta Coll, Xavier (2004)
Article
Open AccessWe study the set M of pairs (f; V ), defined by an endomorphism f of Fn and a d dimensional f–invariant subspace V . It is shown that this set is a smooth manifold that defines a vector bundle on the Grassmann manifold. ... 
Stability of (A,B)invariant subspaces
Peña Carrera, Marta; Puerta Coll, Xavier; Puerta Sales, Ferran (2005)
Article
Open AccessGiven a pair of matrices (A;B) we study the stability of their invariant subspaces from the geometry of the manifold of quadruples (A;B; S; F) where S is an (A;B)invariant subspace and F is such that (A + BF)S ½ S. In ...