A Classification of Nodes for Structural Controllability

In this paper, we consider (large and complex) interconnected networks. We assume that each state/node, not belonging to a set of forbidden nodes of the network, can be selected to act as a steering node, meaning that such a node then is influenced by its own individual control. We aim to achieve structural controllability and we present a classification of the associated steering nodes as being essential (always required to be present), useful (present in certain configurations), and useless (never necessary in whatever configuration). The classification is based on two types of decomposition that naturally show up in the context of the two conditions (connection condition and rank condition) for structural controllability. The underlying methods are related to well known and efficient network algorithms.