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Necessary and sufficient conditions for identifiability of interconnected subsystems

Identifiability conditions refers to the information required, beyond input-output data, to identify the structure of the system. Since there are different ways to describe a system mathematically, there are different notions of structure associated with a single system. In this work we detail the identifiability conditions of interconnected subsystems, referred to as structured linear fractional transformations. The identifiability conditions of the structured linear fractional transformation are then compared to those of the dynamical structure function, another partial system representation, whose cost for identification was detailed in previous work [1]. Both representations appear to detail the same notions of structure of a system; however, this works demonstrates that the cost of identification of the structured linear fractional transformation is always higher than that of the dynamical structure function.