Modification of the Youla-Kucera parameterization for linear mechanical systems subject to non-smooth impacts

A class of n-degrees of freedom fully actuated mechanical systems subject to non-smooth impacts is considered, for which only the position coordinates are available for feedback. A family of compensators is proposed, by suitably modifying the Youla-Kucera parameterization of all stabilizing compensators. By means of Lyapunov techniques, it is proven that, under mild assumptions, all the compensators belonging to the proposed family guarantee the exponential stability of the origin (which corresponds to a condition of contact), and the BIBS (bounded-input bounded-state) stability for the closed-loop system