Approximation of Multivariable Linear Systems with Impulse Response and Autocorrelatlon Sequences

Abstract

This paper considers the construction of approximants of multi-input-output, discrete-time linear systems from the finite data of the impluse response and autocorrelation sequences (or cross correlation between input and output, and autocorrelation of output). In the approximation of multivariable linear systems, it is common practice to use the impluse response sequenceThis is formally equivalent to the Padé approximation technique, which may produce unstable approximants, even though the original system is stable. Mullis and Roberts proposed a new method, which yields stable appr0ximants, in connection with the approximation of digital filters. This is, however, restricted to the single input-output case. This paper extends their method to the multi-input-output case and shows a fast recursive algorithm to construct stable approximants of linear systems