Model comparison and simplification

In this paper we study the comparison and simplification of models given as linear fractional transformations on structured operator sets. Previous simplification results have generalised the method of balanced truncation to such models, including the computation of error bounds, based on solutions to linear matrix inequalities (LMIs). In this paper we show that the previously obtained error bounds hold for a much larger class of simplification methods. These new results can be interpreted as providing a generalisation of both balanced truncation and singular perturbation approximation in a single reduction algorithm