Partial least-squares Padé reduction with exact retention of poles and zeros

Abstract

This paper presents a procedure which allows the exact retention of poles and/or zeros in a reduced-order model while the rest of the coefficients are calculated by means of least-squares matching of Padé coefficients and Markov parameters. The exact retention of poles and zeros is desirable in some situations as a means to use a priori information to determine the simplified model, and thus provide some physical links with the original system. Moreover, the stability of the reduced-order models is guaranteed, although unstable poles and non-minimum phase zeros may be retained if required. On the other hand, least-squares moment-matching is advantageous because extra dynamical information is included in the final model and a family of models of the same order may be readily computed. In this paper the H∞ norm of the error is used to select the best individual from a family of models. The importance of retaining dominant poles and zeros, as well as how to recognize truly dominant poles, is also addressed in the paper. Three numerical examples illustrate the new procedure.