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Mathematical Problems in Engineering
Volume 2014, Article ID 292813, 9 pages
Research Article

Differentiable Families of Planar Bimodal Linear Control Systems

Departament de Matemàtica Aplicada I, ETSEIB, Universitat Politècnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain

Received 18 October 2013; Revised 19 December 2013; Accepted 19 December 2013; Published 22 January 2014

Academic Editor: Hamid Reza Karimi

Copyright © 2014 Josep Ferrer et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.