Approximation of linear systems under the constraint of steady-state values of the step responses

Abstract

This paper considers the construction of approximants of a linear system whose steady-state values of the step responses are identical with those of the original system. It proposes two methods, the constrained least-squares approximation method and the modified least-squares approximation method. The former has a fast recursive algorithm for obtaining approximants, but may produce unstable approximants even though the original system is stable. The latter always yields stable approximants, but requires much more multiplications than the former for obtaining approximants. A simulation example is shown to illustrate the results of the two proposed methods.