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 -class functions. The notion of outer functions (or functions of minimum phase) is extended to matrix-valued functions of the Nevanlinna class , and a canonical factorization theorem for matrix functions of class 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.