  In this paper, a nonlinear extension of the Georgiou-Smith system is
considered and robustness results are proved for a class of nonlinear PI
controllers with respect to fast parasitic first-order dynamics. More
specifically, for a perturbed nonlinear system with sector bounded nonlinearity
and unknown control direction, sufficient conditions for global boundedness and
attractivity have been derived. It is shown that the closed loop system is
globally bounded and attractive if (i) the unmodelled dynamics are sufficiently
fast and (ii) the PI control gain has the Nussbaum function property. For the
case of nominally unstable systems, the Nussbaum property of the control gain
appears to be crucial. A simulation study confirms the theoretical results.
