Tracking control of nonsmooth complementarity Lagrangian systems

In this paper we study the tracking control of Lagrangian systems subject to frictionless unilateral constraints. The stability analysis incorporates the hybrid and nonsmooth dynamical feature of the overall system. The difference between tracking control for unconstrained systems and unilaterally constrained ones, is explained in terms of closed-loop desired trajectories and control signals. This work provides details on the conditions of existence of a controller which guarantees asymptotic stability.