Stabilization of simple mechanical systems subject to inequality constraints

The problem of stabilizing a contact configuration of a one-degree-of-freedom mechanical system subject to a single inequality constraint is considered. By means of Lyapunov techniques it is shown that a PD-like state feedback control law achieves exponential stability and BIBS stability of the desired equilibrium, for either elastic or inelastic impacts. Apart from the theoretical result, simulations and experiments confirm the satisfactory behaviour of the proposed control law.