Reduction of model sets with inclusion

The problem of model set reduction with inclusion is formulated for the purpose of simplifying the design of robust control systems. The problem is solved for the model described by linear fractional transformation with a generalized plant and uncertainty. We introduce a new notion of model set inclusion in our model set reduction problem so that the reduced model set of smaller degree has to include the original model set. A necessary and sufficient condition for this inclusion to hold was found in terms of a structured singular value inequality. A computationally tractable method for model set reduction is obtained for a special case - a single-input single-output additive perturbed plant. The effectiveness of our method was demonstrated by numerical examples