Linear systems with transfer functions of bounded type: Canonical factorization

This paper deals with linear discrete-time systems with matrix-valued transfer functions each entry of which is represented as a quotient of two
H^{\infty}
-class functions. The notion of outer functions (or functions of minimum phase) is extended to matrix-valued functions of the Nevanlinna class
N
, and a canonical factorization theorem for matrix functions of class
N
is presented. This theorem gives minimum phase systems for these linear systems, and specifies a necessary and sufficient condition for the systems to be causal. The notion of the matrix-fraction descriptions (MFD's) is extended to these systems, and some properties of the MFD's are presented by means of the canonical factorization theorem.