A Parametrization of Linear Discrete-Time Systems Interpolating Input-Output Characteristics

Abstract

Problems of finding linear systems which are consistent with given input-output characteristics are important in system approximation, model reduction and system identification. A conventional problem among them is the partial realization problem. In this paper, we consider a problem of finding MIMO linear discrete-time systems interpolating given input-output characteristics. The input-output characteristics are given by coefficients of the Taylor series of the transfer function at some complex points in the unit circle. Thus our problem is a generalization of the partial realization problem. Here, we provide a parametrization of all the interpolating systems with a norm constraint and a parametrization of all the stable interpolating systems.