We analyse the steady-state behaviour of a class of cross-directional controllers that are pertinent to general web-forming processes. Our analysis is framed in terms of the controllable space prescribed by the interaction matrix and general discrete orthonormal basis descriptions of both the input and output spaces under the assumption of closed-loop stability. The specific choice of controller defines (whether explicitly or implicitly) an additional assumed controlled space. It is well known that the controllable space determines a lower bound on output variation. We examine the implications of integral action and provide sufficient conditions for the steady-state output variation to achieve this lower bound. For model-based control with no model-mismatch we confirm some intuitive results that connect the optimal constrained and unconstrained steady state solutions. Model mismatch is usually detrimental to steady state performance. We interpret this effect in terms of leakage between the controllable and assumed controlled spaces, as well as their respective orthogonal complements.