Robust PI control of hysteretic systems

Stability, tracking and the trajectories of a class of hysteretic systems controlled by a PI controller is considered. The system output (not its derivative) is measured and controlled. Only a simple bound on the controller gain parameter is assumed. The closed-loop system is BIBO-stable with a finite gain of one. Furthermore, provided that the desired output is within the limits of the system output, the system will track a constant reference input with zero steady-state error. A bound on the time required to achieve a specified error is obtained.