System identification from a frequency response

This paper considers the problem of approximating a possibly infinite-dimensional multi-input multi-output (MIMO) system by a finite-dimensional system. Unlike most methods which appear in the literature, the method discussed here does not assume a priori knowledge of an analytic expression (i.e. transfer function). An L² approximation problem is formulated and a closed form solution is presented. Several examples are provided in order to demonstrate the shortcomings as well as the positive aspects of the technique. The examples include a delay system, a damped Euler-Bernoulli Beam, and a model of F-8 aircraft