Model Reduction of Linear Continuous Systems Using Impulse-Response Grammians

Abstract

A new algorithm for model reduction of SISO linear continuous systems is proposed. It is based on the impulse-response grammians introduced in [6] for stable linear continous systems. The models are obtained by direct truncation or by the singular perturbation technique. The reduced-order models are stable if the original system is stable. Further, if the direct truncation technique is used, then the first k Markov parameters of the original system and the first k × k elements of the impulse-response grammian are matched. If the singular perturbation technique is used, then the first time moment, the first k-1 Markov parameters and the first k elements of the impulse-response grammian are matched. The method is illustrated by a numerical example and is compared with well known model reduction techniques.