Recently, significant interest has been raised in the study of hybrid systems. In this paper we analyse the performance of some hybrid controls to stabilize a model problem, comparing it with classical methods. We used computer simulations as well as analytic arguments which revealed the presence of periodic orbits for the considered hybrid dynamics. Existence and stability of the latter have also been considered in the framework of a single dynamical system on a suitable manifold (indeed, a stratified set), called the hybrid manifold.