  We demonstrate with a minimal example that in Filippov systems (dynamical
systems governed by discontinuous but piecewise smooth vector fields) stable
periodic motion with sliding is not robust with respect to stable singular
perturbations. We consider a simple dynamical system that we assume to be a
quasi-static approximation of a higher-dimensional system containing a fast
stable subsystem. We tune a system parameter such that a stable periodic orbit
of the simple system touches the discontinuity surface: this is the so-called
grazing-sliding bifurcation. The periodic orbit remains stable, and its local
return map becomes piecewise linear. However, when we take into account the
fast dynamics the local return map of the periodic orbit changes qualitatively,
giving rise to, for example, period-adding cascades or small-scale chaos.
