Persistence of periodic orbits with sliding or sewing by singular perturbation

In this paper we deal with piecewise smooth singularly perturbed systems. We study the effect of singular perturbation when the phase portrait of the reduced problem has periodic orbits with sliding or sewing points. Counter-examples are used to show that in general, only one parameter is not sufficient to ensure the persistence of periodic orbits. With an additional parameter, derived from the Sotomayor-Teixeira regularization, we get conditions which guarantee the persistence.