Minimal‐order transfer functions of dynamical multi‐agent consensus systems

This study deals with transfer functions of a multi‐agent consensus system, composed of identical linear time‐invariant dynamical agents. Motivated by the fact that stabilisation of a single agent in a multi‐agent consensus system with an exogenous controller results in collective stability of all agents, the authors study transfer function representation of a controlled agent in a consensus system. It is shown that the transfer function order of a controlled agent is always greater than double the transfer function order of an isolated agent and that the smallest double order is realised if and only if a controlled agent has inter‐agent connections with all other agents of a consensus system.