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