The Computation of Gram Matrix via Impulse-Response Grammians

The Gram matrix of the system is very useful in modelreduction applications. The computation of this matrix involves evaluation of scalar product of repeated integrals and can be computed in frequency domain as shown in [3, 6]. In this paper a time-domain method for evaluation of the Gram matrix is presented. The method is based on impulse-response Grammians [1, 2] and is considerably simpler than the existing frequency-domain techniques. The method is also illustrated by a numerical example.