  Standard problem of one-degree-of-freedom mechanical systems with Coulomb
friction is revised for a relay-based feedback stabilization. It is recalled
that such a system with Coulomb friction is asymptotically stabilizable via a
relay-based output feedback, as formerly shown in [1]. Assuming an upper
bounded Coulomb friction disturbance, a time-optimal gain of the relay-based
feedback control is found by minimizing the derivative of the Lyapunov function
proposed in [2] for the twisting algorithm. Furthermore, changing from the
discontinuous Coulomb friction to a more physical discontinuity-free one, which
implies a transient presliding phase at motion reversals, we analyze the
residual steady-state oscillations. This is in the sense of stable limit
cycles, in addition to chattering caused by the actuator dynamics. The
numerical examples and an experimental case study accompany the provided
analysis.
