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• Miniversal deformations of observable marked matrices

Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
Mathematical methods in the applied sciences
Vol. 37, num. 1, p. 20-31
DOI: 10.1002/mma.2780
Date of publication: 2014
Journal article

Given the set of vertical pairs of matrices ${\cal M}\subset M_{m,n}(\mathbb C)\times M_n(\mathbb C)$ keeping the subspace $\mathbb C^d\times\{0\}\subset\mathbb C^n$ invariant,we compute miniversal deformations of a given pair when it is observable, and the subspace $\mathbb C^d\times\{0\}$ is marked. Moreover, we obtain the dimension of the orbit, characterize the structurally stable vertical pairs, and study the effect of each deformation parameter. Copyright © 2013 JohnWiley & Sons, Ltd.

Given the set of vertical pairs of matrices ${\cal M}\subset M_{m,n}(\mathbb C)\times M_n(\mathbb C)$ keeping the subspace $\mathbb C^d\times\{0\}\subset\mathbb C^n$ invariant,we compute miniversal deformations of a given pair when it is observable, and the subspace $\mathbb C^d\times\{0\}$ is marked. Moreover, we obtain the dimension of the orbit, characterize the structurally stable vertical pairs, and study the effect of each deformation parameter. Copyright © 2013 JohnWiley & Sons, Ltd.

• Differentiable families of planar bimodal linear control systems

Ferrer Llop, Jose; Magret Planas, Maria Dels Dolors; Peña Carrera, Marta
Mathematical problems in engineering
Vol. 2014, num. Article ID 292813, p. 1-9
DOI: 10.1155/2014/292813
Date of publication: 2014-06
Journal article

We consider bimodal linear control systems consisting of two subsystems acting on each side of a given hyperplane, assuming continuity along it. For a differentiable family of planar bimodal linear control systems, we obtain its stratification diagram and, if controllability holds for each value of the parameters, we construct a differentiable family of feedbacks which stabilizes both subsystems for each value of the parameters.

We consider bimodal linear control systems consisting of two subsystems acting on each side of a given hyperplane, assuming continuity along it. For a differentiable family of planar bimodal linear control systems, we obtain its stratification diagram and, if controllability holds for each value of the parameters, we construct a differentiable family of feedbacks which stabilizes both subsystems for each value of the parameters.

• Determinant of any matrix that belongs to Z(J)

Ferrer Llop, Jose; Mingueza, David; Montoro López, Maria Eulalia
Meeting on Computer Algebra and Applications
p. 111-114
Presentation's date: 2014-06-18
Presentation of work at congresses

• Closed orbits in planar bimodal linear systems

Ferrer Llop, Jose; Peña Carrera, Marta; Susin Sanchez, Antonio
International Linear Algebra Society Conference
Presentation's date: 2014-08-08
Presentation of work at congresses

• Controllability of continuous bimodal linear systems

Ferrer Llop, Jose; Pacha Andujar, Juan Ramon; Peña Carrera, Marta
Mathematical problems in engineering
Vol. 2013, p. 1-14
DOI: 10.1155/2013/342548
Date of publication: 2013-05-01
Journal article

We consider bimodal linear systems consisting of two linear dynamics acting on each side of a given hyperplane, assuming continuity along the separating hyperplane. We prove that the study of controllability can be reduced to the unobservable case, and for these ones we obtain a simple explicit characterization of controllability for dimensions 2 and 3, as well as some partial criteria for higher dimensions

We consider bimodal linear systems consisting of two linear dynamics acting on each side of a given hyperplane, assuming continuity along the separating hyperplane. We prove that the study of controllability can be reduced to the unobservable case, and for these ones we obtain a simple explicit characterization of controllability for dimensions 2 and 3, as well as some partial criteria for higher dimensions.

• Determinant of a matrix that commutes with a Jordan matrix

Montoro López, Maria Eulalia; Ferrer Llop, Jose; Mingueza, David
Linear algebra and its applications
Vol. 439, num. 12, p. 3945-3954
DOI: 10.1016/j.laa.2013.10.023
Date of publication: 2013-10-30
Journal article

Let F be an arbitrary field, Mn(F) the set of all matrices n×n over F and J¿Mn(F) a Jordan matrix. In this paper, we obtain an explicit formula for the determinant of any matrix that commutes with J, i.e., the determinant of any element T¿Z(J), the centralizer of J. Our result can also be extended to any T'¿Z(A), where A¿Mn(F), can be reduced to J=S-1AS. This is because T=S-1T'S¿Z(J), and clearly View the MathML source. If F is algebraically closed, any matrix A can be reduced in this way to a suitable J. In order to achieve our main result, we use an alternative canonical form W¿Mn(F) called the Weyr canonical form. This canonical form has the advantage that all matrices K¿Z(W) are upper block triangular. The permutation similarity of T¿Z(J) and K¿Z(W) is exploited to obtain a formula for the determinant of T. The paper is organized as follows: Section 2 contains some definitions and notations that will be used through all the paper. In Section 3, matrices T¿Z(J) are described and the determinant of T is computed in a particular case. In Section 4, we recall the Weyr canonical form W of a matrix and the corresponding centralizer Z(W). A formula to compute the determinant of any K¿Z(W) is rewritten. Finally, in Section 5 an explicit formula for the determinant of any T¿Z(J) is obtained.

Let F be an arbitrary field, Mn(F) the set of all matrices n×n over F and J∈Mn(F) a Jordan matrix. In this paper, we obtain an explicit formula for the determinant of any matrix that commutes with J, i.e., the determinant of any element T∈Z(J), the centralizer of J. Our result can also be extended to any T′∈Z(A), where A∈Mn(F), can be reduced to J=S−1AS. This is because T=S−1T′S∈Z(J), and clearly View the MathML source. If F is algebraically closed, any matrix A can be reduced in this way to a suitable J. In order to achieve our main result, we use an alternative canonical form W∈Mn(F) called the Weyr canonical form. This canonical form has the advantage that all matrices K∈Z(W) are upper block triangular. The permutation similarity of T∈Z(J) and K∈Z(W) is exploited to obtain a formula for the determinant of T. The paper is organized as follows: Section 2 contains some definitions and notations that will be used through all the paper. In Section 3, matrices T∈Z(J) are described and the determinant of T is computed in a particular case. In Section 4, we recall the Weyr canonical form W of a matrix and the corresponding centralizer Z(W). A formula to compute the determinant of any K∈Z(W) is rewritten. Finally, in Section 5 an explicit formula for the determinant of any T∈Z(J) is obtained.

• Structural stability of planar bimodal linear systems

Ferrer Llop, Jose; Peña Carrera, Marta; Susin Sanchez, Antonio
International Conference on Numerical Analysis and Applied Mathematics
p. 2205-2208
DOI: 10.1063/1.4825976
Presentation's date: 2013-09
Presentation of work at congresses

We consider bimodal linear dynamical systems consisting of two linear dynamics acting on each side of a given hyperplane, assuming continuity along the separating hyperplane. Focusing in the planar case, we describe which of these systems are structurally stable

We consider bimodal linear dynamical systems consisting of two linear dynamics acting on each side of a given hyperplane, assuming continuity along the separating hyperplane. Focusing in the planar case, we describe which of these systems are structurally stable.

• Differentiable families of stabilizers for planar bimodal linear control systems

Ferrer Llop, Jose; Magret Planas, Maria Dels Dolors; Peña Carrera, Marta
International Conference on Numerical Analysis and Applied Mathematics
p. 2068-2071
DOI: 10.1063/1.4825942
Presentation's date: 2013-09
Presentation of work at congresses

We consider bimodal linear control systems consisting of two subsystems acting on each side of a given hyperplane, assuming continuity along the separating hyperplane. For a differentiable family of controllable planar ones, we construct a differentiable family of feedbacks which point wise stabilizes both subsystems

We consider bimodal linear control systems consisting of two subsystems acting on each side of a given hyperplane, assuming continuity along the separating hyperplane. For a differentiable family of controllable planar ones, we construct a differentiable family of feedbacks which pointwise stabilizes both subsystems.

• Perturbations preserving conditioned invariant subspaces

Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
Mathematical methods in the applied sciences
Vol. 35, num. 3, p. 249-371
DOI: 10.1002/mma.1553
Date of publication: 2012-02
Journal article

Given the set of matrix pairsM Mm,n.C/ Mn.C/ keeping a subspace S Cn invariant, we obtain a miniversal deformation of a pair belonging to an open dense subset ofM. It generalizes the known results when S is a supplementary subspace of the unobservable one.

• Learning automation to teach mathematics

Ferrer Llop, Jose; Peña Carrera, Marta; Ortiz Caraballo, Carmen
DOI: DOI: 10.5772/2327
Date of publication: 2012-07
Book chapter

• Miniversal deformations of observable marked matrices

Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
Date: 2012
Report

Given the set of vertical pairs of matrices M¿ Mm,n(C)×Mn(C) keeping the subspace Cd×{0} ¿ Cn invariant, we compute miniversal deformations of a given pair when it is observable and the subspace Cd × {0} is marked. Moreover, we obtain the dimension of the orbit, characterize the structurally stable vertical pairs and study the effect of each deformation parameter.

• Classification of monogenic invariant subspaces and uniparametric linear control systems

Compta Creus, Albert; Ferrer Llop, Jose
DOI: MTM 2011-23892
Date: 2012-12
Report

The classification of the invariant subspaces of an endomorphism has been an open problem for a long time, and it is a ”wild” problem in the general case. Here we obtain a full classification for the monogenic ones. Some applications are derived: in particular, canonical forms for uniparametric linear control systems, non necessarily controllable, with regard to linear changes of state variables

• Estructuras geométricas de los sistemas de control lineales, lineales a trozos y sistemas conmutados

Compta Creus, Albert; Clotet Juan, Jose; Garcia Planas, Maria Isabel; Magret Planas, Maria Dels Dolors; Peña Carrera, Marta; Puerta Coll, Francisco Javier; Montoro López, Maria Eulalia; Puerta Sales, Fernando; Ferrer Llop, Jose
Competitive project

• Stabilization of controllable planar bimodal linear systems

Peña Carrera, Marta; Ferrer Llop, Jose
SIAM Conference on Applied Linear Algebra
p. 146
Presentation's date: 2012-06-21
Presentation of work at congresses

• Clasificación de los subespacios invariantes monogenerados

Compta Creus, Albert; Ferrer Llop, Jose
Encuentro de Álgebra Lineal, Análisis Matricial y Aplicaciones
p. 33
Presentation's date: 2012-06
Presentation of work at congresses

• Geometric structure of single/combined equivalence classes of a controllable pair

Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
Electronic journal of linear algebra
Vol. 22, p. 1112-1128
Date of publication: 2011-11
Journal article

Given a pair of matrices representing a controllable linear system, its equivalence classes by the single or combined action of feedbacks, change of state and input variables, as well as their intersection are studied. In particular, it is proved that they are differentiable manifolds and their dimensions are computed. Some remarks concerning the effect of different kinds of feedbacks are derived.

• On the effect of friend feedbacks

Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
Mathematical methods in the applied sciences
Vol. 34, num. 3, p. 309-314
DOI: 10.1002/mma.1357
Date of publication: 2011
Journal article

Given S an (A,B)-invariant subspace, we prove that the set of friend feedbacks is a linear variety, which can be considered as the direct sum of the feedbacks of the restriction to S and the co-restriction to S ⊥. In particular, when the natural controllability hypothesis hold, both pole assignments are simultaneously possible bymeans of a convenient friend feedback. Copyright

• Estructuras geométricas de los sistemas lineales de control y su extensión a los sistemas conmutados

Clotet Juan, Jose; Montoro López, Maria Eulalia; Peña Carrera, Marta; Compta Creus, Albert; Puerta Coll, Francisco Javier; Puerta Sales, Fernando; Garcia Planas, Maria Isabel; Magret Planas, Maria Dels Dolors; Ferrer Llop, Jose
Competitive project

• Orbit stratification of non-controllable bimodal systems

Peña Carrera, Marta; Ferrer Llop, Jose; Magret Planas, Maria Dels Dolors
Conference of the International Linear Algebra Society
p. 57
Presentation's date: 2011-08-23
Presentation of work at congresses

• Contribución al estudio de los subespacios invariantes

Compta Creus, Albert; Ferrer Llop, Jose
Congreso de Ecuaciones Diferenciales y Aplicaciones y Congreso de Matemàtica Aplicada
Presentation's date: 2011-09-06
Presentation of work at congresses

• Planar bimodal piecewise linear systems. Bifurcation diagrams

Ferrer Llop, Jose; Magret Planas, Maria Dels Dolors; Pacha Andujar, Juan Ramon; Peña Carrera, Marta
Vol. 51, p. 55-63
Date of publication: 2010
Journal article

• Learning engineering to teach mathematics

Ferrer Llop, Jose; Peña Carrera, Marta; Ortiz Caraballo, Carmen
Frontiers in education conference
num. S1J, p. 1-6
DOI: /fie-conference.org/fie2010/papers/1207.pdf
Date of publication: 2010-10
Journal article

• Local differentiable pole assignment

Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
Linear and multilinear algebra
Vol. 58, num. 5, p. 563-569
DOI: 10.1080/03081080902745304
Date of publication: 2010
Journal article

Given a general local differentiable family of pairs of matrices, we obtain a local differentiable family of feedbacks solving the pole assignment problem, that is to say, shifting the spectrum into a prefixed one. We point out that no additional hypothesis is needed. In fact, simple approaches work in particular cases (controllable pairs, constancy of the dimension of the controllable subspace, and so on). Here the general case is proved by means of Arnold’s techniques: the key point is to reduce the construction to a versal deformation of the central pair; in fact to a quite singular miniversal one for which the family of feedbacks can be explicitly constructed. As a direct application, a differentiable family of stabilizing feedbacks is obtained, provided that the central pair is stabilizable.

• Bimodal piecewise linear dynamical systems. Reduced forms

Ferrer Llop, Jose; Magret Planas, Maria Dels Dolors; Peña Carrera, Marta
International journal of bifurcation and chaos
Vol. 20, num. 9, p. 2795-2808
DOI: 10.1142/S0218127410027362
Date of publication: 2010
Journal article

• Output regulation problem for differentiable families of linear systems

Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
Mathematical problems in engineering
Vol. 2010, num. ID 698548, p. 1-9
DOI: 10.1155/2010/698548
Date of publication: 2010
Journal article

Given a family of linear systems depending on a parameter varying in a differentiable manifold, we obtain sufficient conditions for the existence of a (global or local) differentiable family of controllers solving the output regulation problem for the given family. Moreover, we construct it when these conditions hold.

• Learning technology to teach mathematics

Ferrer Llop, Jose; Peña Carrera, Marta; Ortiz Caraballo, Carmen
American Mathematical Society. National Meeting
Presentation of work at congresses

• Perturbations preserving conditioned invariant subspaces

Peña Carrera, Marta; Compta Creus, Albert; Ferrer Llop, Jose
International Conference on Circuits, Systems, Signals
p. 204-210
Presentation's date: 2010-09
Presentation of work at congresses

Given the set of matrix pairs M ⊂ Mm,n(C) × Mn(C) keeping a subspace S ⊂ Cn invariant, we obtain a miniversal deformation of a pair belonging to an open dense subset of M. It generalizes the known results when S is a supplementary subspace of the unobservable one.

• Miniversal Deformations of Bimodal Picewise Linear Systems

Ferrer Llop, Jose; Magret Planas, Maria Dels Dolors; Pacha Andujar, Juan Ramon; Peña Carrera, Marta
Meeting on Linear Algebra Matrix Analysis and Applications
p. 1-6
Presentation's date: 2010-06
Presentation of work at congresses

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.

Keywords: Bimodal piecewise linear system, miniversal deformations, reduced forms.

• Distance from a controllable switched linear system to an uncontrollable one

Clotet Juan, Jose; Ferrer Llop, Jose; Magret Planas, Maria Dels Dolors
Meeting on Linear Algebra Matrix Analysis and Applications
p. 1-7
Presentation's date: 2010-06-02
Presentation of work at congresses

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.

• A lower bound for the distance from a controllable switched linear system to an uncontrollable one

Clotet Juan, Jose; Ferrer Llop, Jose; Magret Planas, Maria Dels Dolors
Conference of the International Linear Algebra Society
p. 55
Presentation's date: 2010-06-20
Presentation of work at congresses

• Computation of canonical forms and miniversal deformations of bimodal dynamical systems

Peña Carrera, Marta; Ferrer Llop, Jose; Magret Planas, Maria Dels Dolors; Pacha Andujar, Juan Ramon
Conference of the International Linear Algebra Society
p. 16
Presentation of work at congresses

• Learning engineering to teach mathematics

Ferrer Llop, Jose; Peña Carrera, Marta; Ortiz, Carmen
Annual Frontiers in Education Conference
p. 1-6
DOI: /fie-conference.org/fie2010/papers/1207.pdf
Presentation's date: 2010-10-27
Presentation of work at congresses

The Bologna process is a good opportunity to bring together first-year mathematics courses of engineering degrees and technology courses offered in subsequent years. In fact, the Faculty Council has decided that 20% of the credits from basic courses must be related to technological applications. To this end, during the past academic year a mathematical engineering seminar was held with each session dealing with one technological discipline. The main goal of the seminar, which relied on the presence of speakers from both mathematics and engineering departments, was to identify the most commonly used mathematical tools. Furthermore, a set of exercises and some guidelines addressed to faculty lacking an engineering background were created. Here, we present some of this material: first, a summary of the collection of exercises illustrating the use of Linear Algebra in different engineering areas such as Mechanical Engineering, Control and Automation, and second, some exercises

• Geometric structure of the equivalence classes of a controllable pair

Peña Carrera, Marta; Compta Creus, Albert; Ferrer Llop, Jose
International Conference on Circuits, Systems, Signals
p. 211-218
Presentation's date: 2010-09
Presentation of work at congresses

Given a pair of matrices representing a controllable linear system, we study its equivalence classes by the single or combined action of feedbacks and change of state and input variables, as well as their intersections. In particular, we prove that they are differentiable manifolds and we compute their dimensions. Some remarks concerning the effect of different kinds of feedbacks are derived.

• On the effect of friend feedbacks

Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
AIP Conference proceedings
Vol. 1168, num. 3, p. 564-567
DOI: 10.1063/1.3241524
Date of publication: 2009
Journal article

Given S an (A;B)-invariant subspace, we prove that the set of friend feedbacks is a (nm¡md+dq)-dimensional linear variety, which can be considered as the direct sum of the feedbacks of the restriction to S and the co-restriction to S?. In particular, if (A;B) is controllable and S is a controllability subspace, both pole assignments are simultaneously possible by means of a convenient friend feedback.

• Output regulation problem for differentiable families of linear systems

Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
AIP Conference proceedings
Vol. 1168, p. 49-52
DOI: 10.1063/1.3241507
Date of publication: 2009
Journal article

Given a family of linear systems depending on a parameter varying in a differentiable manifold, we obtain sufficient conditions for the existence of a (global or local) differentiable family of controllers solving the output regulation problem for the given family. Moreover, we construct it when these conditions hold.

• Switched singular linear systems

Clotet Juan, Jose; Ferrer Llop, Jose; Magret Planas, Maria Dels Dolors
Mediterranean Conference on Control and Automation
p. 1343-1347
DOI: 10.1109/MED.2009.5164733
Presentation's date: 2009-06
Presentation of work at congresses

We consider switched singular linear systems and determine the set of reachable/controllable states. We derive necessary and sufficient conditions for such a system to be reachable/controllable when an “equisingularity condition” holds.

• Stratification and bifurcation diagrams of bimodal piecewise linear dynamical system

Ferrer Llop, Jose; Magret Planas, Maria Dels Dolors; Pacha Andujar, Juan Ramon; Peña Carrera, Marta
Int. conference of non-autonomous and stochastic dynamical systems, and multidisciplinary applications (NSDS'09)
p. 30
Presentation's date: 2009-06
Presentation of work at congresses

• Use of reduced forms in the disturbance decoupling problem

Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
Linear algebra and its applications
Vol. 430, num. 5-6, p. 1574-1589
DOI: 10.1016/j.laa.2008.04.033
Date of publication: 2009-03
Journal article

Specific algorithms, such as those involving the supremal of the invariant subspaces contained in a suitable subspace, are known to be able to test whether a disturbance decoupling problem (DDP) is solvable. Here, by reducing the system to its Molinari form, we obtain an alternative description of this supremal object and compute its dimension. Hence we have a general result for solving the decoupling provided that a Molinari basis is known. In particular, a necessary numerical condition for it is derived. The same technique is applied to the DDPS, that is, when stability of the decoupled closed loop system is required.

• Bimodal Piecewise linear systems. Reduced forms

Ferrer Llop, Jose; Magret Planas, Maria Dels Dolors; Peña Carrera, Marta
International Workshop on dynamical systems and multidisciplinary applications
Presentation of work at congresses

• Geometric Structure of the equivalence classes of a controllable pair

Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
International Linear Algebra Society (ILAS). Conference
Presentation of work at congresses

• Perturbations preserving conditioned invariant subspaces

Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
International Linear Algebra Society (ILAS). Conference
Presentation of work at congresses

• Use of reduced forms in the disturbance decoupling problem

Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
Date: 2008-04
Report

• Geometría de las perturbaciones de sistemas lineales de control

Puerta Coll, Francisco Javier; Compta Creus, Albert; Magret Planas, Maria Dels Dolors; Peña Carrera, Marta; Clotet Juan, Jose; Ferrer Llop, Jose; Puerta Sales, Fernando
Competitive project

• Estructura diferenciable de las clases de equivalencia de un par controlable

Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
Congreso de Ecuaciones Diferenciales y Aplicaciones / Congreso de Matemática Aplicada
p. 1-8
Presentation of work at congresses

• Realización de perturbaciones

Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
Séptimo Encuentro Plenario de Teoría de Sistemas
Presentation's date: 2007-01-01
Presentation of work at congresses

• Use of reduced forms in the disturbance decoupling problem

Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
International Linear Algebra Society (ILAS). Conference
p. 6
Presentation of work at congresses

• Uso de formas reducidas en el "disturbance decoupling problem"

Ferrer Llop, Jose
Séptimo Encuentro Plenario de Teoría de Sistemas
Presentation's date: 2007-01-01
Presentation of work at congresses

• Local differentiable pole assignment

Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
Date: 2007-02
Report

• Geometric structure of the equivalence classes of a controllable pair

Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
Date: 2007-05
Report