Common Zero Structure of Rational Matrix Functions

The paper is concerned with description of common zero data of two square size rational matrix functions. The notion of a common null pair, which encodes the data, is introduced and studied from various points of view. The main result of the paper is a characterization of the common null pair in terms of realization of the functions in question. Connections with common minimal divisors of rational matrix functions are elucidated. The recently developed theory of null-pole triples and Sylvester data sets is extensively used in the proofs.