Convex formulations for data-based uncertainty minimization of linear uncertainty models

Convex formulations are derived for the minimization of uncertainty bounds with respect to a nominal model and given input-output data for general uncertainty models of LFT type. The known data give rise to data-matching conditions that have to be satisfied. It is shown how these conditions, which originally are in the form of BMIs for a number of uncertainty models, can be transformed to LMIs, thus making the optimization problem convex. These formulations make it easy to find the best uncertainty model from a number of alternatives for robust control design.