Behavioral controllability and coprimeness for pseudorational transfer functions

Controllability plays various crucial roles in behavioral system theory. While there exist several characterizations of this notion, in terms of the Bézout identity, image representation, direct sum decomposition, etc., its overall picture for infinite-dimensional systems still remains rather incomplete, in spite of various existing attempts. This article gives an extension of such results in a well-behaved class of infinite-dimensional systems, called pseudorational. A proper choice of an algebra makes the treatment more transparent. We establish equivalent conditions for controllability in terms of the Bézout identity, relationships with notions such as image representation and direct sum decompositions.