Robust stability analysis of Cross-Directional Processes using the v-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 will be based on the identified model,the effect of theses uncertainties on stability must be addressed. The v-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 v-gap stability theorem to check stability conditions provided by the multidimensional digital filter stability theory. A simulation example is presented to illustrate the technique.