In this paper we investigate the limitations of adaptive pole placement control of AR systems when an additive disturbance is present. The magnitude of the disturbance is dependent on past input and output values. It is shown that the control objective of robust stabilization restricts the set of systems one can deal with. We subsequently propose and analyze an adaptive algorithm which can be applied to convex, not necessarily bounded, subsets of the aforesaid set. In particular, it is shown that all signals in the control loop remain bounded.