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We consider third-order dynamic systems which have integral feedback actionand discontinuous relay disturbance. More specifically for applications, ourfocus is on the integral plus state-feedback control of motion systems withdiscontinuous Coulomb-type friction. We resume the attractive stiction region,where the hybrid system has also solutions in Filippov sense and the motiontrajectories remain in an idle state (that we call `stiction') until thesliding-mode condition becomes violated by an integral action. We analyze theconditions for occurrence of the slowly converging stick-slip cycles. We alsoshow that the hybrid system is globally but only asymptotically and almostalways not exponentially stable. A particular case of exponential convergencecan appear for some initial values, assuming the characteristic equation of thelinear subsystem has only the real roots. Illustrative numerical examples areprovided alongside with the developed analysis.

On convergence analysis of feedback control with integral action and discontinuous relay perturbation