  We consider third-order dynamic systems which have integral feedback action
and discontinuous relay disturbance. More specifically for applications, our
focus is on the integral plus state-feedback control of motion systems with the
discontinuous Coulomb-type friction. We resume the attractive stiction region,
where the hybrid system has also solutions in Filippov sense, while the motion
trajectories remain in an idle state (that we call `stiction') until the
sliding-mode condition becomes violated through the integral action. We analyze
the conditions for occurrence of the slowly converging stick-slip cycles. We
also show that the hybrid system is globally but only asymptotically and almost
always not exponentially stable. A particular case of exponential convergence
can appear for some initial values, assuming the characteristic equation of the
linear subsystem has only the real roots. Illustrative numerical examples are
provided alongside with the developed analysis.
