Minimal realization of discrete linear systems from input-output observations

A direct procedure is presented for obtaining a minimal realization of a multiple-input multiple-output linear time-invariant discrete system from observations of the input and output. Discussion is limited to the case of noise-free observations in order to focus attention on the realization procedure and to display the structure of the resulting realization. This known structural form car be used as a check on the realization procedure. Application of the procedure requires knowledge of an upper bound on the minimal system dimension; however, a modification is given to handle the situation where an upper bound is not known. An example is included to show the operation of the procedure.