Approximation of multivariable linear systems with impulse response and autocorrelation sequences

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