Scalable Controllability Analysis of Structured Networks

This article deals with strong structural controllability of structured networks. A structured network is a family of heterogeneous structured systems (called node systems) that are interconnected by means of a structured interconnection law, all given by pattern matrices. Here, we consider structured networks with single-input-single-output node systems. It is shown that such a structured network is strongly structurally controllable if and only if an associated structured system is. This structured system will, in general, have a very large state space dimension and, therefore, existing tests for verifying strong structural controllability are not tractable. The main result of this article circumvents this problem. We show that controllability can be tested by replacing the original network by a new network in which all original node systems have been replaced by (auxiliary) node systems with state space dimensions either 1 or 2. Hence, controllability of the original network can be verified by testing controllability of a structured system with state space dimension at most twice the number of node systems, regardless of the state space dimensions of the original node systems.