Input-output structure and transfer equivalent polynomial representation of behavioural systems

This paper characterizes the transfer matrix for behavioural systems in a general polynomial description. Necessary and sufficient conditions are derived for the existence and uniqueness of the transfer matrix. The characterization is the so-called input-output structure of behavioural systems. A descriptor system form has been proposed and proved to possess the same transfer matrix as a behavioural system in the general polynomial form. When possessing the same transfer matrix, two such system forms are referred to as being transfer equivalent to each other.