Laplacian Dynamics on Cographs: Controllability Analysis through Joins and Unions

TL;DR

This paper analyzes the controllability of Laplacian dynamic networks on cographs, providing necessary and sufficient conditions and an efficient method for selecting minimal control nodes based on sibling partitions.

Contribution

It introduces a novel controllability characterization for cographs using sibling partitions and links modularity with modal properties for network control analysis.

Findings

Controllability depends on sibling partition properties.

Minimal control node sets can be efficiently identified.

Results apply to subclasses of cographs.

Abstract

In this paper, we examine the controllability of Laplacian dynamic networks on cographs. Cographs appear in modeling a wide range of networks and include as special instances, the threshold graphs. In this work, we present necessary and sufficient conditions for the controllability of cographs, and provide an efficient method for selecting a minimal set of input nodes from which the network is controllable. In particular, we define a sibling partition in a cograph and show that the network is controllable if all nodes of any cell of this partition except one are chosen as control nodes. The key ingredient for such characterizations is the intricate connection between the modularity of cographs and their modal properties. Finally, we use these results to characterize the controllability conditions for certain subclasses of cographs.