Single agent control for multi-agent dynamical consensus systems

The problem of controlling a single agent in a multi-agent consensus system is studied in order to make states of all agents in the system follow a common reference signal. It is shown that if every two agents in a given system are connected and a reference signal is a step function, then every controller locally stabilising one single agent gives rise to a successful tracking of all agents. When a proportional control is employed, the relations between overall tracking performance, interconnection topology and the choice of a controlled agent are analytically investigated. A numerical study is also performed to substantiate theoretical findings.