  We propose a model for representing a point mass subject to Coulomb friction
in feedback with a PID controller, based on a differential inclusion comprising
all the possible magnitudes of static friction during the stick phase. For this
model we study the set of all equilibria and we establish its global asymptotic
stability using a discontinuous Lyapunov-like function, and a suitable
LaSalle's invariance principle. We finally use well-posedness of the proposed
model to establish useful robustness results, including an ISS property from a
suitable input in a perturbed context. Simulation results are also given to
illustrate our statements.
