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.
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