Browsing by Author "Puerta Coll, Xavier"

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, Ion (1999)
Article
Open AccessGiven an observable system (C,A)€ K^(mxn)X K^(nxn)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 ... 
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, ... 
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 ... 
Stability of <math>(A, B)</math>invariant subspaces
Puerta Sales, Ferran; Puerta Coll, Xavier (2003)
External research report
Open AccessGiven a pair of matrices (A,B) we study the stability of their invariant subspaces from a geometric point of view. The main tool is the manifold of quadruples((A;B); F; S) where S is an (A,B)invariant subspace and F is ... 
Stratification and bundle structure of the set of conditioned invariant subspaces in the general case
Ferrer Llop, Josep; Puerta Sales, Ferran; Puerta Coll, Xavier (2000)
Article
Open AccessWe 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 ... 
Stratification and bundle structure of the set of conditioned invariant subspaces in the general case
Ferrer Llop, Josep; Puerta Sales, Ferran; Puerta Coll, Xavier (2003)
Article
Open AccessWe 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 ... 
Stratification and bundle structure of the set of conditioned invariant subspaces in the general case
Ferrer Llop, Josep; Puerta Sales, Ferran; Puerta Coll, Xavier (1999)
Article
Open AccessWe extend some known results about the smooth stratification of the set of conditioned invariant subspaces for a general pair (C,A)€C^nXC^(n+m) without any assumption on the observability. More precisely we prove that the ...