Now showing items 1-20 of 31

• #### 1. Inauguració ﻿

(2011-02-22)
Audiovisual
Open Access
• #### A cellular decomposition of the manifold of observable conditioned invariant subspaces ﻿

(2000)
Article
Open Access
Given 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 ﻿

(2001-02)
Article
Open Access
Given 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 ﻿

(1999)
External research report
Open Access
• #### A sufficient condition for Lipschitz stability of controlled Invariant subspaces ﻿

(2009-12)
Article
Restricted access - publisher's policy
Given 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 ...
• #### Brunovsky local form of a holomorphic family of pair of matrices ﻿

(Elsevier, 1997)
Article
Restricted access - publisher's policy
Following Arnold’s techniques, we obtain a local canonical form of a holomorphic family of pairs of matrices ( A( A), B(h)) ac t e d on by the state feedback group. We obtain an explicit formula to compute the dimension ...
• #### Global block-similarity and pole assignment of class C<sup>p</sup> ﻿

(1998)
Article
Open Access
Starting from the existence of a $C^{p}$-basis for any $C^{p}$-family of subspaces having constant dimension, we construct a Brunovsky basis of class $C^{p}$ for a $C^{p}$-family of pairs of matrices having constant ...
• #### Global reduction to the Kronecker canonical form of a C^r-family of time-invariant linear systems ﻿

(1999)
Article
Open Access
We present a geometric approach to the study of time-invariant 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, ...
• #### Miniversal deformations of marked matrices ﻿

(2001)
Article
Open Access
Given the set of square matricesM⊂Mn+m(C) that keep the subspace W = Cnx{0} ⊂ Cn+m invariant, we obtain the implicit form of a miniversal deformation of a matrix a∈M, and we compute it explicitely when this matrix is ...
• #### On the geometry of the generalized partial realization problem ﻿

(2010-09)
Article
Restricted access - publisher's policy
The 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 ﻿

(2003)
Article
Open Access
For 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 ﻿

(2004)
Article
Open Access
Given 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 ﻿

(2003)
Article
Open Access
Given 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 ﻿

(Servicio de publicaciones de la UPV, 2010)
Conference lecture
Open Access
Given 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 ﻿

(2001)
Article
Open Access
• #### Output Maximal Dimension for the Disturbance Decoupling Problem ﻿

(2001)
Article
Open Access
Given a linear time invariant system with a disturbance we describe a method of finding the maximal dimensional output for a generic Disturbance Decoupling problem.
• #### Regularity of the Brunovsky-Kronecker stratification ﻿

(1998)
Article
Open Access
We study the partition of the set of pairs of matrices according to the Brunovsky- Kronecker type. We show that it is a constructible stratification, and that it is Whitney regular when the second matrix is a column matrix. ...
• #### Sistemes lineals: una aproximació a algun dels seus conceptes i problemes rellevants ﻿

(2014-01-10)
Other
Open Access
L'objectiu que m'he proposat al preparar aquesta exposició ha estat el de mostrar. per una banda, com alguns dels problemes bàsics de la teoria de Sistemes Dinàmics Lineals tenen una resposta senzilla en termes de l' ...
• #### Stability of (A,B)-invariant subspaces ﻿

(2005)
Article
Open Access
Given 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 $(A, B)$-invariant subspaces ﻿

(2003)
External research report
Open Access
Given 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 ...