Normally Hyperbolic Sets in Discontinuous Dry Friction Oscillator

In this paper, we study a four-parameters piecewise-smooth dry friction oscillator from Control theory. Using Filippov's convention, we prove the existence of a codimension-1 bifurcation which gives rise to a normally hyperbolic set composed by a family of attracting cylinders. This bifurcation exhibits interesting discontinuous oscillation phenomena. We also present consistent numerical simulations.