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This paper deals with strong structural controllability of structurednetworks. A structured network is a family of structured systems (called nodesystems) that are interconnected by means of a structured interconnection law.The node systems and their structured interconnection law are given by patternmatrices. It is shown that a structured network is strongly structurallycontrollable if and only if an associated structured system is. This structuredsystem will in general have a very large state space dimension, and thereforeexisting tests for verifying strong structural controllability are nottractable. The main result of this paper circumvents this problem. We show thatcontrollability can be tested by replacing the original network by a newnetwork in which all original node systems have been replaced by (auxiliary)node systems with state space dimensions either 1 or 2. Hence, controllabilityof the original network can be verified by testing controllability of astructured system with state space dimension at most twice the number of nodesystems, regardless of the state space dimensions of the original node systems.

Scalable controllability analysis of structured networks