Robust Stability Analysis of Cross-Directional Processes using the U-gap metric

In this paper, a robust stability criterion is proposed for cross-directional processes. Modeling uncertainties resulting from input-output identification are inevitable and as control design is based on the identified model, the effect of theses uncertainties on stability must be addressed. The nu-gap metric is convenient to investigate robust stability in a closed-loop configuration. The CD process is modeled by a spatial static non-causal transfer function in the cross-direction (CD) and a dynamic causal model in the main direction (MD). As the CD process is analogous to a 2D spatially non-causal digital filter, robust stability of the 2D process is investigated by employing the nu-gap stability theorem to check stability conditions provided by the multidimensional digital filter stability theory. A simulation example is presented to illustrate the technique