Model Reduction Methods Taking Account of Positive Realness and Minimum-Phase Properties

Abstract

This paper is concerned with model reduction methods taking account of positive realness and minimum-phase properties, while keeping the H infinity norm of the associated error system (||E(s)||)as small as possible with the LMI optimization technique. These methods are applied to the reduction of an Euler-Bernoulli beam system to demonstrate their effectiveness.In the application of the proposed methods,we first need to obtain apositive real or minimum-phase reduced-order model such that ||E(s)|| is reasonably small.A way for obtaining such a reduced-order modelis via the truncated positive real balanced realization method,but it sometimes leads toa reduced-order model with very large ||E(s)||.Thus, this paper also tackles this problem from the numerical pointof view.