Matrix-function descriptions and the quasi-McMillan form of a transfer function of bounded type

This paper deals with linear discrete-time systems with matrix-valued transfer functions each entry of which is represented as a quotient of two analytic functions of the Hardy class . Such transfer functions are referred to as being of bounded type [3]. The notions of matrix-fraction descriptions (MFD\´s) and irreducible MFD\´s are examined for a transfer function of bounded type. Making use of Nordgren\´s results on the quasi-equivalence of matrices over [1], the quasiMcMillan form is proposed for a transfer function of bounded type. It is shown that all the numerators of right or left irreducible MFD\´s of possess the same invariant factors, and that all the denominators of right or left irreducible MFD\´s of possess the same invariant factors except unity invariant factors.