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

摘要

We consider the set of bimodal linear systems consisting of two lineardynamics acting on each side of a given hyperplane, assuming continuity alongthe separating hyperplane. Focusing on the unobservable planar ones, we obtaina simple explicit characterization of controllability. Moreover, we apply thecanonical forms of these systems depending on two state variables to obtainexplicitly miniversal deformations, to illustrate bifurcation diagrams and toprove that the unobservable controllable systems are stabilizable. Preprint of an article submitted for consideration in IJBC \copyright 2011copyright World Scientific Publishing Company http://www.worldscinet.com/ijbc/