Representation and reduction of model sets

The problem of model set reduction with inclusion is formulated for the purpose of simplifying the design of robust control systems. We are concerned with uncertain systems modeled by the homographic transformation of the generator and the uncertainty. The generator is a rational transfer function matrix by which the model set is defined. The uncertainty is assumed to be linear time invariant and bounded. We achieve a model set reduction by simplifying its generator in such a way that the resulting new model set includes the original one. A necessary and sufficient condition for model set inclusion is found by an infinite dimensional matrix inequality of generators under some conditions. Using state-space representation of generators, this inequality can be transformed to a matrix inequality under stronger condition. A computationally tractable method for model set reduction is obtained for a special case, single input single output, additive perturbed plant. A numerical example is studied in order to show computational procedures of our method.