Using Kautz Models in Model Reduction

摘要

A method is presented for model reduction. It is based on the representation of the original model in an (exact) Kautz series. The Kautz series consists of orthogonalized exponential sequences. The Kautz series is non-unique: it depends on the ordering of the poles. The ordering of the poles can be chosen such that the first terms contribute most to the overall impulse response of the original system in a quadratic sense. Having a specific ordering, the reduced model order, say n, can be chosen by considering the energy contained in a truncated representation. The resulting reduced order model is obtained simply by truncation of the Kautz series at the nth term. Since only a selection of the poles already present in the original model is made, the numerical problems associated with the calculation of the optimal poles are avoided. The model order reduction method is illustrated by two examples. In the first example the Kautz model order reduction method is compared with the balanced model order reduction technique. In the second example, the Kautz model reduction method is combined with Prony's method to estimate exponential sequences from a noisy data set.