Model reduction by state truncation with applications to compensator reduction

In this paper, we consider the model reduction of stable transfer functions given by n(s) = C(s-A)-1B, C ?? Rm??n, A ?? Rn??n, B ?? Rn??p and study the reduced order models obtained by truncating some states. For this class of models, we show that the reduced order model is stable if an auxiliary transfer function has a stable inverse. We introduce a subclass of such reductions called positive-real reduction which preserves stability and show that the balanced reduction [1, 2] is a special case of this. We also provide bounds on the error at each frequency. We apply the reduction procedure to the reduction of feedback controllers and show that the reduction is possible if the order of the controller exceeds that of the plant.