Integral control with saturating input

In this paper we consider the problem of integral low-gain control of stable finite-dimensional, single-input single-output systems with positive steady-state gain. The linear plant is subject to a sector-bounded actuator nonlinearity such as saturation or dead-zone. We show that provided the integral gain is small enough then the closed-loop system is globally stable, and arbitrary stepped reference signals are asymptotically tracked by the system output. The value of the gain needed is smaller than that required for closed loop stability without the actuator nonlinearity and is computed graphically from a Nyquist contour plot of the series connection of the system and an integrator.