Model reduction of linear continuous systems using weighted impulse response Gramians

A new algorithm for model reduction of SISO linear continuous systems is proposed. It is based on the weighted impulse response Gramians. The reduction algorithm yields a family of stable reduced order models for different weighting factors in the weighted impulse response Gramian. The model corresponding to the weight of zero, matches the impulse response norm of the original system and its derivatives exactly. The method is illustrated by a numerical example and is compared with well known model reduction techniques.