Network controllability of structured networks: a survey on graph-theoretical approaches

This paper provides an extensive overview of research on the controllability of linear structured networks. In structured networks, the connection weight between agents is characterized as either a fixed zero or any non-zero value, leading to numerous possible realizations. We refer to these non-zero values of connection weights within structured networks as network parameters. Such structured networks exhibit control uncertainty due to variations in network parameters. This paper delves into this aspect, offering insights into how changes in the network parameters affect the controllability of a structured network. By reviewing graph-theoretical results from the past decade, this paper introduces a hierarchical approach to controllability that addresses both entire graphs and individual nodes. Finally, this paper highlights unresolved issues in the field of structured network controllability and suggests future directions.