Robustness of the nonlinear PI control method to ignored actuator dynamics

This note examines the robustness properties of the nonlinear PI control method to ignored actuator dynamics. It is proven that global boundedness and regulation can be achieved for sector bounded nonlinear systems with unknown control directions if the actuator dynamics are sufficiently fast and the nonlinear PI control gain is chosen from a subclass of the Nussbaum function class. Simulation examples are also presented that demonstrate the validity of our arguments.