Unobservable Planar Bimodal Linear Systems: Miniversal Deformations, Controllability and Stabilization

Details Unobservable Planar Bimodal Linear Systems: Miniversal Deformations, Controllability and Stabilization Unobservable Planar Bimodal Linear Systems: Miniversal Deformations, Controllability and Stabilization

2011-12-30

arxiv.org/abs/1201.0113v1

Mathematics

Dynamical Systems

18 pages, 3 figures

Scientific paper

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. Preprint of an article submitted for consideration in IJBC \copyright 2011 copyright World Scientific Publishing Company http://www.worldscinet.com/ijbc/

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