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 EGSA  Differential Equations, Geometry, Control and Dynamical Systems, and Applications
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 Department of Applied Mathematics I
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 Barcelona School of Industrial Engineering (ETSEIB)
 marta.penyaupc.edu
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Controllability of continuous bimodal linear systems
Ferrer Llop, Jose; Pacha Andujar, Juan Ramon; Peña Carrera, Marta
Mathematical problems in engineering
Date of publication: 20130501
Journal article
Read the abstract View Share Reference managersWe 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. 
Structural stability of planar bimodal linear systems
Ferrer Llop, Jose; Peña Carrera, Marta; Susin Sanchez, Antonio
International Conference on Numerical Analysis and Applied Mathematics
Presentation's date: 201309
Presentation of work at congresses
Read the abstract View Share Reference managersWe 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
Presentation's date: 201309
Presentation of work at congresses
Read the abstract View Share Reference managersWe 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
Date of publication: 201202
Journal article
Read the abstract View Share Reference managersGiven 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
Date of publication: 201207
Book chapter
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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
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Miniversal deformations of observable marked matrices
Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
Date: 2012
Report
Read the abstract View Share Reference managersGiven 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. 
Stabilization of controllable planar bimodal linear systems
Peña Carrera, Marta; Ferrer Llop, Jose
SIAM Conference on Applied Linear Algebra
Presentation's date: 20120621
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Realizations of perturbations of an observable pair with prescribed indices
Beitia, M.A.; Compta Creus, Albert; de Hoyos, Inmaculada; Peña Carrera, Marta
Linear algebra and its applications
Date of publication: 2011
Journal article
Read the abstract View Share Reference managersIt is well known that, when a full rank observable pair (C,A) is slightly perturbed, the new observability indices k′ are majorized by the initial ones k, k≻k′. Conversely, any indices k′ majorized by k can be obtained by perturbing (C,A). The aim of this paper is the explicit construction of perturbations of (C,A) which have the desired indices k′ by means of a sequence of uniparametrical versal perturbations. Even more, using versal deformations we refine this construction in such a way that the perturbation has the maximum possible number of zeros and no parameters in the square part. 
On the effect of friend feedbacks
Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
Mathematical methods in the applied sciences
Date of publication: 2011
Journal article
Read the abstract View Share Reference managersGiven 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 corestriction to S ⊥. In particular, when the natural controllability hypothesis hold, both pole assignments are simultaneously possible bymeans of a convenient friend feedback. Copyright 
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
Date of publication: 201111
Journal article
Read the abstract View Share Reference managersGiven 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. 
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
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Orbit stratification of noncontrollable bimodal systems
Peña Carrera, Marta; Ferrer Llop, Jose; Magret Planas, Maria Dels Dolors
Conference of the International Linear Algebra Society
Presentation's date: 20110823
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Bimodal piecewise linear dynamical systems. Reduced forms
Ferrer Llop, Jose; Magret Planas, Maria Dels Dolors; Peña Carrera, Marta
International journal of bifurcation and chaos
Date of publication: 2010
Journal article
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Planar bimodal piecewise linear systems. Bifurcation diagrams
Ferrer Llop, Jose; Magret Planas, Maria Dels Dolors; Pacha Andujar, Juan Ramon; Peña Carrera, Marta
Boletín de la Sociedad Española de Matemática Aplicada
Date of publication: 2010
Journal article
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Output regulation problem for differentiable families of linear systems
Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
Mathematical problems in engineering
Date of publication: 2010
Journal article
Read the abstract View Share Reference managersGiven 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 engineering to teach mathematics
Ferrer Llop, Jose; Peña Carrera, Marta; Ortiz Caraballo, Carmen
Frontiers in education conference
Date of publication: 201010
Journal article
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Local differentiable pole assignment
Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
Linear and multilinear algebra
Date of publication: 2010
Journal article
Read the abstract View Share Reference managersGiven 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. 
Learning technology to teach mathematics
Ferrer Llop, Jose; Peña Carrera, Marta; Ortiz Caraballo, Carmen
American Mathematical Society. National Meeting
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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
Presentation's date: 201009
Presentation of work at congresses
Read the abstract View Share Reference managersGiven 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. 
Learning engineering to teach mathematics
Ferrer Llop, Jose; Peña Carrera, Marta; Ortiz, Carmen
Annual Frontiers in Education Conference
Presentation's date: 20101027
Presentation of work at congresses
Read the abstract View Share Reference managersThe Bologna process is a good opportunity to bring together firstyear 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 
The change of feedback invariants under column perturbations: particular cases
Asunción, M Beitia; Compta Creus, Albert; Inmaculada, De Hoyos; Peña Carrera, Marta
Linear and multilinear algebra
Date of publication: 201001
Journal article
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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
Presentation's date: 201006
Presentation of work at congresses
Read the abstract View Share Reference managersBimodal 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. 
Perturbations preserving conditioned invariant subspaces
Peña Carrera, Marta; Compta Creus, Albert; Ferrer Llop, Jose
International Conference on Circuits, Systems, Signals
Presentation's date: 201009
Presentation of work at congresses
Read the abstract View Share Reference managersGiven 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. 
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
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On the effect of friend feedbacks
Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
AIP Conference proceedings
Date of publication: 2009
Journal article
Read the abstract View Share Reference managersGiven 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 corestriction 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
Date of publication: 2009
Journal article
Read the abstract View Share Reference managersGiven 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. 
A sufficient condition for Lipschitz stability of controlled Invariant subspaces
Peña Carrera, Marta; Puerta Sales, Fernando; Puerta Coll, Francisco Javier
Mediterranean journal of mathematics
Date of publication: 200912
Journal article
Read the abstract View Share Reference managersGiven 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 an (A,B)invariant subspace and F a corresponding feedback. 
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 nonautonomous and stochastic dynamical systems, and multidisciplinary applications (NSDS'09)
Presentation's date: 200906
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Differentiable structure of the set of coaxial stressstrain tensors
Clotet Juan, Jose; Magret Planas, Maria Dels Dolors; Peña Carrera, Marta
Mathematical methods in the applied sciences
Date of publication: 200909
Journal article
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Use of reduced forms in the disturbance decoupling problem
Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
Linear algebra and its applications
Date of publication: 200903
Journal article
Read the abstract View Share Reference managersSpecific 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. 
Deformaciones miniversales de parejas de tensores de segundo orden
Clotet Juan, Jose; Magret Planas, Maria Dels Dolors; Peña Carrera, Marta
Date of publication: 200807
Book chapter
Read the abstract View Share Reference managersConsideramos en el espacio de parejas de tensores tension y deformacion la relacion de equivalencia que se corresponde con cambios de base ortonormales. Identificandolas con parejas de matrices cuadradas, podemos utilizar la tecnica de las deformaciones miniversales para averiguar, dada una pareja de tensores cualquiera, cuales son las parejas de tensores que se pueden obtener al perturbar ligeramente la dada, puesto que las clases de equivalencia se pueden identificar con las orbitas que resultan al actuar un grupo de Lie sobre la variedad diferenciable de las parejas de matrices simetricas y son, por lo tanto, variedades diferenciables. Presentamos también las dimensiones que son posibles para dichas orbitas. 
Miniversal deformations of pairs of symmetric secondorder tensors in the context of solid mechanics
Clotet Juan, Jose; Magret Planas, Maria Dels Dolors; Peña Carrera, Marta
Date of publication: 200807
Book chapter
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Use of reduced forms in the disturbance decoupling problem
Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
Date: 200804
Report
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Differentiable Structure of the Set of Coaxial StressStrain Tensors
Clotet Juan, Jose; Magret Planas, Maria Dels Dolors; Peña Carrera, Marta
Date: 200801
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A sufficient condition for stability of controlled invariant subspaces
Peña Carrera, Marta; Puerta Sales, Fernando; Puerta Coll, Francisco Javier
Date of publication: 200807
Book chapter
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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
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Perturbations preserving conditioned invariant subspaces
Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
International Linear Algebra Society (ILAS). Conference
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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
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Realizations of perturbations of an observable pair with prescribed indices
Beitia, M A; Compta Creus, Albert; Hoyos, I; Peña Carrera, Marta
Encuentro de Algebra Lineal, Análisis Matricial y aplicaciones
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Local differentiable pole assignment
Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
Date: 200702
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Geometric structure of the equivalence classes of a controllable pair
Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
Date: 200705
Report
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Output Regulation Problem for Differentiable Families of Linear Systems
Compta Creus, Albert; Peña Carrera, Marta; Griñó, R
Date: 200707
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The change of feedback invariants under column perturbations: particular cases
Asuncion, M Beitia; Compta Creus, Albert; Inmaculada, De Hoyos And Marta Peña; Peña Carrera, Marta
Date: 200709
Report
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Realización de perturbaciones
Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
Séptimo Encuentro Plenario de Teoría de Sistemas
Presentation's date: 20070101
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Use of reduced forms in the disturbance decoupling problem
Compta Creus, Albert; Ferrer Llop, Jose; Peña Carrera, Marta
International Linear Algebra Society (ILAS). Conference
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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
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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
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Deformaciones miniversales de tensores y parejas de tensores simétricos
Peña Carrera, Marta
Séptimo Encuentro Plenario de Teoría de Sistemas
Presentation's date: 20070101
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A sufficient condition for stability of controlled invariant subspaces
Peña Carrera, Marta; Puerta Sales, Fernando; Puerta Coll, Francisco Javier
International Conference of Numerical Analysis and Applied Mathematics 2007
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