A simple adaptive PI controller for linear systems with constant disturbances

It is known that an adaptive controller via high-gain output feedback can globally stabilize a class of minimum phase systems with relative degree one. However, exact output regulation is difficult for systems with disturbances. In this paper, we consider linear single-input/single-output (SISO) systems with unknown constant disturbances. We present a simple adaptive output feedback controller with an integral action and show that it can asymptotically stabilize those disturbed systems. The proposed PI-type adaptive controller can also deal with the output tracking problem of a step reference.