Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Controllability plays various crucial roles in behavioral system theory. While there exist several characterizations of this notion, in terms of the Bezout 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 ll-behaved class of infinite-dimensional systems, called pseudorational. A proper choice of an algebra makes the treatment more transparent.  establish equivalent conditions for controllability in terms of the Bezout identity, relationships with notions such as image representation and direct sum decompositions.
['Yutaka Yamamoto']
I am writing a research paper on a idea Behavioral controllability and coprimeness for pseudorational transfer functions
[{"from": "human", "value": "I am writing a research paper on a idea Behavioral controllability and coprimeness for pseudorational transfer functions"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Controllability plays various crucial roles in behavioral system theory. While there exist several characterizations of this notion, in terms of the Bezout 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 ll-behaved class of infinite-dimensional systems, called pseudorational. A proper choice of an algebra makes the treatment more transparent.  establish equivalent conditions for controllability in terms of the Bezout identity, relationships with notions such as image representation and direct sum decompositions."}]