  Planar switched system with dead-zone are analyzed. In particular, we
consider the effects of perturbation of the linear control law from purely
positional to position-velocity control. This type of perturbation leads to a
novel Hopf-like discontinuity induced bifurcation. We show that this
bifurcation leads to the creation of small scale limit cycle attractors, which
scale as the square root of the bifurcation parameter. We note that a Hopf-like
bifurcation analyzed in non-smooth systems is characterized by a linear scaling
law. We then investigate numerically a planar switched system with positional
feedback law, dead-zone and time delay in the switching function. Using the
same parameter values as for the switched system without delay in the switching
function, we show numerically a Hopf-like bifurcation scenario which matches
qualitatively and quantitatively with the scenario analyzed for the non-delayed
system.
