On optimal approximation of high-order linear systems by low-order models

An engineering solution to the problem of approximating a high-order linear system by a low-order model is suggested, which consists in formulating a quadratic error functional as a basic tool for the construction of a physically transparent and practically meaningful approximation criterion. For various different modes of operation analytical expressions for the evaluation of the functional as well as the gradients with respect to the unknown model parameters are given, which allows known gradient techniques to be applied for finding the optimal model parameters. In addition a representation for a general multivariate model, using only the minimal number of unknown parameters, is given.