Use of non-smooth impacts for the control of (otherwise) uncontrollable linear mechanical systems

A class of under actuated linear mechanical systems subjected to non-smooth impacts was considered to solve the dead-beat regulation problem. A pair of inequality constraints was considered to describe the mechanical system with n-degrees of freedom. A hybrid compensator combining a discrete-time rationale and a continuous-time implementation was used to analyze static state-feedback control law for the closed loop system. Analysis suggested that the discrete-time control law relied on the possibility of planning in real time and the measurement of state of overall system after impact time