Minimal realization of discrete linear systems from input/output observations

A direct procedure is presented for obtaining a minimal realization of a linear, time invariant, discrete system from observations of input and output. It is shown that the procedure can be used for almost any input sequence. Application of the procedure requires knowledge of an upper bound on the minimal system dimension; a modification is given to handle the situation where an upper bound is not known. The structure of the realization obtained is displayed and can be used as a check on the realization. An example is included to show the operation of the procedure.