Model reduction of linear discrete systems via weighted impulse response Grammians

A new method for model reduction of linear discrete systems is proposed. It is based on the weighted impulse response Grammians. These Grammians are extensions of ones proposed for linear continuous systems and contain information on the input-output behavior of the system. The reduced-order models are obtained by retaining the states corresponding to the dominant eigenvalues of these Grammians and are stable if the original system is stable. The method is illustrated by a numerical example and is compared with well-known model reduction techniques. The results obtained using this method are similar to those obtained using the balanced realization technique