System Theoretic Aspects of Influenced Consensus: Single Input Case

This technical note examines the dynamics of networked multi-agent systems operating with a consensus-type algorithm, under the influence of an attached node or external agent. Depending on the specific scenario, the attached node can be viewed as a network intruder or an administrator. We introduce an influence scheme, naive of the network topology, involving predictable excitation of the network with the objective of manipulating, disrupting, or steering its evolution. The spectrum of the corresponding Dirichlet matrix provides bounds on the system-theoretic properties of the resulting influenced network, quantifying its security-or viewed differently-its manageability. Finally, the controllability gramian for influenced consensus is examined, providing insights into its H₂-norm and controllability properties.