In this paper, it is shown that using a low dimensional non-linear predictive control scheme, provably stable limit cycles can be obtained for open-loop non-linear systems with unstable equilibrium point. A particular case, where the limit cycle may be reduced to a single point in the state space, can be obtained, which corresponds to asymptotic stabilization. The system may present hybrid nature in the sense that discontinuities ( jump phenomena) on the state evolution may be handled. The proposed feedback scheme holds for classical jump-free systems as a particular case. The proposed strategy is illustrated through two examples: a jump-free system ( the ball and beam) and a non-linear hybrid dynamical system including state jumps ( the modified impulsive Lorenz chaotic system).