Now showing items 1-20 of 26

• #### 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 ﻿

(1999)
Article
Open Access
Given 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 ﻿

(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 ...
• #### Classification and versal deformation of generalized flags ﻿

(2003)
Article
Open Access
A 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^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, ...
• #### 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 ...

(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.
• #### Perturbation of quadrics ﻿

(2000)
Article
Open Access
The 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 ﻿

(2004)
Article
Open Access
We 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 ﻿

(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 ...
• #### Stratification and bundle structure of the set of conditioned invariant subspaces in the general case ﻿

(2000)
Article
Open Access
We 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 ﻿

(2003)
Article
Open Access
We 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 ﻿

(1999)
Article
Open Access
We 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 ...