In this report we discuss the design of cross-directional controllers which are guaranteed to be robustly stabilizing while incorporating a quadratic programme for steady state performance. The report is loosely based on the technical report of Akkermans (2003) who proposes using the multivariable circle criterion to guarantee closed-loop stability of cross-directional controllers in the presence of sector-bounded non-linearities. Heath and Wills (2004) recommend implementing cross-directional controllers in modal form with a constrained internal model control (IMC) structure; nominal optimal steady state performance is guaranteed via a non-linear element that incorporates a quadratic programme. Finally Heath et al. (2003) observe that the quadratic programme suggested by Heath and Wills (2004) is itself a sector bounded non-linearity.