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
H^{\infty}
. 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
H(z)
of bounded type. Making use of Nordgren's results on the quasi-equivalence of matrices over
H^{\infty}
[1], the quasiMcMillan form is proposed for a transfer function
H(z)
of bounded type. It is shown that all the numerators of right or left irreducible MFD's of
H(z)
possess the same invariant factors, and that all the denominators of right or left irreducible MFD's of
H(z)
possess the same invariant factors except unity invariant factors.