Model Reduction using Impulse-Response Gramians: A Frequency-Domain Approach

A frequency domain model reduction technique based on the impulse-response gramian is proposed. Two new methods for evaluation of the impulse-response gramian in the frequency domain are also presented. The Routh technique relies on a Routh table to evaluate energy integrals of the type found on the impulse-response gramian diagonal, while the second approach uses an Inners determinant technique. Off diagonal elements are computed via system Markov parameters and knowledge of diagonal values. The model reduction technique, involving truncation of the impulse-response gramian, is a variation on that presented by Agathoklis and Sreeram (1990 a). The proposed method evaluates the transfer function of the reduced-order model directly rather than producing a state spare representation. Algorithms outlining the steps involved in impulse-response gramian evaluation, plus those for model reduction, are given. Each is supported by a numerical example.