Abstract
In this paper, it is shown that using a low dimensional predictive control scheme, provably stable limit cycles can be obtained for open-loop unstable nonlinear systems. Asymptotic stabilization is obtained as a particular case where the limit cycle reduces to a single point in the state space. The system may present hybrid nature in the sense that discontinuities 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: the ball and beam (A classical jump-free system) and an under-actuated biped walking robot (a system with hybrid dynamic including state jumps).