Robust Stability Analysis of Constrained Cross-Directional Control via Integral Quadratic Constraints

A robust stability test for a class of constrained cross-directional controllers is proposed. The cross-directional controller involves a quadratic program embedded within an internal model control structure and achieves optimal steady-state performance when the plant is fully known. Both the non-linearity in the controller and the unmodeled plant dynamics satisfy certain integral quadratic inequalities. This allows us to obtain conditions for robust stability that can be expressed as linear matrix inequalities via the KYP lemma. Circumstances in which the results can be exploited to decompose the control design into modes are also discussed