Finding Conditions for Target Controllability under Christmas Trees

This paper presents new graph-theoretic conditions for structural target controllability of directed networks. After reviewing existing conditions and highlighting some gaps in the literature, we introduce a new class of network systems, named Christmas trees, which generalizes trees and cacti. We then establish a graph-theoretic characterization of sets of nodes that are structurally target controllable for a simple subclass of Christmas trees. Our characterization applies to general network systems by considering spanning subgraphs of Christmas tree class and allows us to uncover target controllable sets that existing criteria fail to identify.