Irreducible Jordan form realization of a rational matrix

This paper presents a new method for realizing a rational transfer function matrix into an irreducible Jordan canonical form state equation. The method consists of two steps, first, to form a controllable state equation and then secondly, to obtain a controllable as well as observable realization by nonsingular transformations. If every denominator of the rational matrix is given in the factored form, then the proposed method can be carried out quite easily.