M. Dolors Magret | Universitat Politecnica de Catalunya (original) (raw)
Papers by M. Dolors Magret
2013 National Security Days (JNS3), 2013
In this paper we consider two models of concatenated convolutional codes from the perspective of ... more In this paper we consider two models of concatenated convolutional codes from the perspective of linear systems theory. We present an input-state-output representation of these models and we study the conditions for control properties as controllability, observability as well as output observability.
Linear and Multilinear Algebra, 1998
A generalized Sylvester matrix equation is considered. This equation is related with the stabiliz... more A generalized Sylvester matrix equation is considered. This equation is related with the stabilizer of a triple of matrices under the Lie group action on the space of triples of matrices which corresponds to the equivalence relation generalizing, in a natural way, the similarity between square matrices.criterion for the structural stability of a triple of matrices t is deduced in
Linear Algebra and its Applications, 1999
Linear Algebra and its Applications, 2006
In the space M of generalized time-invariant linear systems Eẋ = Ax + Bu we consider two equivale... more In the space M of generalized time-invariant linear systems Eẋ = Ax + Bu we consider two equivalence relations, generalizing block-similarity of pairs (A, B) ∈ M n (C) × M n×m (C). Both equivalence relations can be defined by the action of Lie groups G 1 = Gl(n; C) × Gl(m; C) × M m×n (C) × M m×n (C) and G 2 = Gl(n; C) × G 1 acting on M, α 1 : G 1 × M →M ((P , R, U, V ), (E, A, B)) →(P −1 EP + P −1 BU, P −1 AP + P −1 BV , P −1 BR) α 2 : G 2 × M →M ((P , Q, R, U, V ), (E, A, B)) →(QEP + QBU, QAP + QBV , QBR).
Linear Algebra and its Applications, 1997
We study the perturbations of triples of matrices, and we give explicitly a miniversal deformatio... more We study the perturbations of triples of matrices, and we give explicitly a miniversal deformation. As a corollary we obtain the dimension of the stabilizer and a characterization of the structural stability of triples of matrices, in terms of their numerical invariants. 0 Elsevier Science Inc., 1997 *
International Journal of Modern Physics B, 2012
ABSTRACT We present a geometric approach to the study of singular switched linear systems, defini... more ABSTRACT We present a geometric approach to the study of singular switched linear systems, defining a Lie group action on the differentiable manifold consisting of the matrices defining their subsystems with orbits coinciding with equivalence classes under an equivalence relation which preserves reachability and derive miniversal (orthogonal) deformations of the system. We relate this with some new results on reachability of such systems.
Journal of Mathematical Sciences, 2007
The concept of structural stability, first introduced by A.A. Andronov and L.Pontryagin in 1937 i... more The concept of structural stability, first introduced by A.A. Andronov and L.Pontryagin in 1937 in the qualitative theory of dynamical systems (structurally stable elements being those whose behaviour does not change when applying small perturbations) has been studied by many authors in Control Theory. We present in this work conditions for structurally stable linear time-invariant singular systems when considering different equivalence relations among them.
Linear Algebra and its Applications, 2001
We consider quadruples of matrices (E, A, B, C) defining generalized linear multivariable time-in... more We consider quadruples of matrices (E, A, B, C) defining generalized linear multivariable time-invariant dynamical systems Eẋ(t) = Ax(t) + Bu(t), y(t) = Cx(t) with A, E square matrices and B, C rectangular matrices. Using geometrical techniques we present upper bounds and lower bounds for the distances between a quadruple and the nearest nonstructurally stable, uncontrollable and/or unobservable one, in terms of the singular values of matrices associated to the quadruple. (J. Clotet), igarcia@ma1.upc.es (M.I. García-Planas), dolors@ma1.upc.es (M.D. Magret). 0024-3795/01/$ -see front matter 2001 Elsevier Science Inc. All rights reserved. PII: S 0 0 2 4 -3 7 9 5 ( 0 1 ) 0 0 3 0 4 -4
Linear Algebra and its Applications, 1999
A dynamical system can be represented by
Linear Algebra and its Applications, 2001
We consider quadruples of matrices (E, A, B, C) representing generalized linear multivariable sys... more We consider quadruples of matrices (E, A, B, C) representing generalized linear multivariable systems
We consider switched singular linear systems and conditions for such a system to be reachable/con... more We consider switched singular linear systems and conditions for such a system to be reachable/controllable in the cases where some hypotheses hold.
Advances in Pure Mathematics, 2015
We consider the set of quadruples of matrices defining singular linear time-invariant dynamical s... more We consider the set of quadruples of matrices defining singular linear time-invariant dynamical systems and show that there is a one-to-one correspondence between this set and a subset of the set of polynomial matrices of degree two. This correspondence preserves the equivalence relations introduced in both sets (feedback-similarity and strict equivalence): two quadruples of matrices are feedback-equivalent if, and only if, the polynomial matrices associated to them are also strictly equivalent. We characterize structurally stable polynomial matrices (stable elements under small perturbations) describing singular systems and derive a lower bound on the distance to the orbits of polynomial matrices with strictly lower dimension.
The set of controllable switched linear systems is an open set in the space of all switched linea... more The set of controllable switched linear systems is an open set in the space of all switched linear systems. Then it makes sense to compute the distance from a controllable switched linear system to the set of uncontrollable systems. In this work we obtain an upper bound for such distance.
We consider the set of bimodal linear systems consisting of two linear dynamics acting on each si... more We consider the set of bimodal linear systems consisting of two linear dynamics acting on each side of a given hyperplane, assuming continuity along the separating hyperplane. Focusing on the unobservable planar ones, we obtain a simple explicit characterization of controllability. Moreover, we apply the canonical forms of these systems depending on two state variables to obtain explicitly miniversal deformations, to illustrate bifurcation diagrams and to prove that the unobservable controllable systems are stabilizable. * Partially supported by DGICYT
El conjunt dels nombres enters i el de polinomis amb coeficients en un cos són els exemples més b... more El conjunt dels nombres enters i el de polinomis amb coeficients en un cos són els exemples més bàsics d'anells commutatius, que constitueixen l'essència de l'àlgebra commutativa, branca de les matemàtiques estretament lligada a la geometria algebraica.És a finals del segle XIX que, amb el desenvolupament de l'àlgebra abstracta, els anells de polinomis es van començar a estudiar des d'un nou enfocament. 1
Keywords: Bimodal piecewise linear system, miniversal deformations, reduced forms. Bimodal linear... more Keywords: Bimodal piecewise linear system, miniversal deformations, reduced forms. Bimodal linear systems are those consisting of two linear systems on each side of a given hyperplane, having continuous dynamics along that hyperplane. In this work, we focus on the derivation of (orthogonal) miniversal deformations, by using reduced forms. Postprint (published version)
In the space of singular time invariant linear systems E ˙ x = Ax + Bu we relate miniversal defor... more In the space of singular time invariant linear systems E ˙ x = Ax + Bu we relate miniversal deformations of triples of matrices M = f(E;A;B)g, E;A 2 Mn(C) and B 2 Mm£n(C) representing the systems, under usual two equivalence relations. Both equivalence relations can be defined by the action of a Lie groups G1 = f(P;R;U;V )g and G2 = f(P;Q;R;U;V;)g, P;Q 2 Gl(n;C), R 2 Gl(m;C), U;V 2 Mm£n(C), acting on M.
We give a miniversal deformation of each pair of symmetric matrices (A, B) under congruence; that... more We give a miniversal deformation of each pair of symmetric matrices (A, B) under congruence; that is, a normal form with minimal number of independent parameters to which all matrices (A + E, B + E ′ ) close to (A, B) can be reduced by congruence transformations
2013 National Security Days (JNS3), 2013
In this paper we consider two models of concatenated convolutional codes from the perspective of ... more In this paper we consider two models of concatenated convolutional codes from the perspective of linear systems theory. We present an input-state-output representation of these models and we study the conditions for control properties as controllability, observability as well as output observability.
Linear and Multilinear Algebra, 1998
A generalized Sylvester matrix equation is considered. This equation is related with the stabiliz... more A generalized Sylvester matrix equation is considered. This equation is related with the stabilizer of a triple of matrices under the Lie group action on the space of triples of matrices which corresponds to the equivalence relation generalizing, in a natural way, the similarity between square matrices.criterion for the structural stability of a triple of matrices t is deduced in
Linear Algebra and its Applications, 1999
Linear Algebra and its Applications, 2006
In the space M of generalized time-invariant linear systems Eẋ = Ax + Bu we consider two equivale... more In the space M of generalized time-invariant linear systems Eẋ = Ax + Bu we consider two equivalence relations, generalizing block-similarity of pairs (A, B) ∈ M n (C) × M n×m (C). Both equivalence relations can be defined by the action of Lie groups G 1 = Gl(n; C) × Gl(m; C) × M m×n (C) × M m×n (C) and G 2 = Gl(n; C) × G 1 acting on M, α 1 : G 1 × M →M ((P , R, U, V ), (E, A, B)) →(P −1 EP + P −1 BU, P −1 AP + P −1 BV , P −1 BR) α 2 : G 2 × M →M ((P , Q, R, U, V ), (E, A, B)) →(QEP + QBU, QAP + QBV , QBR).
Linear Algebra and its Applications, 1997
We study the perturbations of triples of matrices, and we give explicitly a miniversal deformatio... more We study the perturbations of triples of matrices, and we give explicitly a miniversal deformation. As a corollary we obtain the dimension of the stabilizer and a characterization of the structural stability of triples of matrices, in terms of their numerical invariants. 0 Elsevier Science Inc., 1997 *
International Journal of Modern Physics B, 2012
ABSTRACT We present a geometric approach to the study of singular switched linear systems, defini... more ABSTRACT We present a geometric approach to the study of singular switched linear systems, defining a Lie group action on the differentiable manifold consisting of the matrices defining their subsystems with orbits coinciding with equivalence classes under an equivalence relation which preserves reachability and derive miniversal (orthogonal) deformations of the system. We relate this with some new results on reachability of such systems.
Journal of Mathematical Sciences, 2007
The concept of structural stability, first introduced by A.A. Andronov and L.Pontryagin in 1937 i... more The concept of structural stability, first introduced by A.A. Andronov and L.Pontryagin in 1937 in the qualitative theory of dynamical systems (structurally stable elements being those whose behaviour does not change when applying small perturbations) has been studied by many authors in Control Theory. We present in this work conditions for structurally stable linear time-invariant singular systems when considering different equivalence relations among them.
Linear Algebra and its Applications, 2001
We consider quadruples of matrices (E, A, B, C) defining generalized linear multivariable time-in... more We consider quadruples of matrices (E, A, B, C) defining generalized linear multivariable time-invariant dynamical systems Eẋ(t) = Ax(t) + Bu(t), y(t) = Cx(t) with A, E square matrices and B, C rectangular matrices. Using geometrical techniques we present upper bounds and lower bounds for the distances between a quadruple and the nearest nonstructurally stable, uncontrollable and/or unobservable one, in terms of the singular values of matrices associated to the quadruple. (J. Clotet), igarcia@ma1.upc.es (M.I. García-Planas), dolors@ma1.upc.es (M.D. Magret). 0024-3795/01/$ -see front matter 2001 Elsevier Science Inc. All rights reserved. PII: S 0 0 2 4 -3 7 9 5 ( 0 1 ) 0 0 3 0 4 -4
Linear Algebra and its Applications, 1999
A dynamical system can be represented by
Linear Algebra and its Applications, 2001
We consider quadruples of matrices (E, A, B, C) representing generalized linear multivariable sys... more We consider quadruples of matrices (E, A, B, C) representing generalized linear multivariable systems
We consider switched singular linear systems and conditions for such a system to be reachable/con... more We consider switched singular linear systems and conditions for such a system to be reachable/controllable in the cases where some hypotheses hold.
Advances in Pure Mathematics, 2015
We consider the set of quadruples of matrices defining singular linear time-invariant dynamical s... more We consider the set of quadruples of matrices defining singular linear time-invariant dynamical systems and show that there is a one-to-one correspondence between this set and a subset of the set of polynomial matrices of degree two. This correspondence preserves the equivalence relations introduced in both sets (feedback-similarity and strict equivalence): two quadruples of matrices are feedback-equivalent if, and only if, the polynomial matrices associated to them are also strictly equivalent. We characterize structurally stable polynomial matrices (stable elements under small perturbations) describing singular systems and derive a lower bound on the distance to the orbits of polynomial matrices with strictly lower dimension.
The set of controllable switched linear systems is an open set in the space of all switched linea... more The set of controllable switched linear systems is an open set in the space of all switched linear systems. Then it makes sense to compute the distance from a controllable switched linear system to the set of uncontrollable systems. In this work we obtain an upper bound for such distance.
We consider the set of bimodal linear systems consisting of two linear dynamics acting on each si... more We consider the set of bimodal linear systems consisting of two linear dynamics acting on each side of a given hyperplane, assuming continuity along the separating hyperplane. Focusing on the unobservable planar ones, we obtain a simple explicit characterization of controllability. Moreover, we apply the canonical forms of these systems depending on two state variables to obtain explicitly miniversal deformations, to illustrate bifurcation diagrams and to prove that the unobservable controllable systems are stabilizable. * Partially supported by DGICYT
El conjunt dels nombres enters i el de polinomis amb coeficients en un cos són els exemples més b... more El conjunt dels nombres enters i el de polinomis amb coeficients en un cos són els exemples més bàsics d'anells commutatius, que constitueixen l'essència de l'àlgebra commutativa, branca de les matemàtiques estretament lligada a la geometria algebraica.És a finals del segle XIX que, amb el desenvolupament de l'àlgebra abstracta, els anells de polinomis es van començar a estudiar des d'un nou enfocament. 1
Keywords: Bimodal piecewise linear system, miniversal deformations, reduced forms. Bimodal linear... more Keywords: Bimodal piecewise linear system, miniversal deformations, reduced forms. Bimodal linear systems are those consisting of two linear systems on each side of a given hyperplane, having continuous dynamics along that hyperplane. In this work, we focus on the derivation of (orthogonal) miniversal deformations, by using reduced forms. Postprint (published version)
In the space of singular time invariant linear systems E ˙ x = Ax + Bu we relate miniversal defor... more In the space of singular time invariant linear systems E ˙ x = Ax + Bu we relate miniversal deformations of triples of matrices M = f(E;A;B)g, E;A 2 Mn(C) and B 2 Mm£n(C) representing the systems, under usual two equivalence relations. Both equivalence relations can be defined by the action of a Lie groups G1 = f(P;R;U;V )g and G2 = f(P;Q;R;U;V;)g, P;Q 2 Gl(n;C), R 2 Gl(m;C), U;V 2 Mm£n(C), acting on M.
We give a miniversal deformation of each pair of symmetric matrices (A, B) under congruence; that... more We give a miniversal deformation of each pair of symmetric matrices (A, B) under congruence; that is, a normal form with minimal number of independent parameters to which all matrices (A + E, B + E ′ ) close to (A, B) can be reduced by congruence transformations