Leader-following state consensus for homogeneous multi-agent systems over time-varying feedback graphs

We study leader-following state consensus for homogeneous multi-agent systems over time-varying network topologies. The agent dynamic systems under our investigation are assumed to be marginally stable and positive real. For the case when the time-varying graph is undirected and piecewise continuous, the leader-following state consensus is shown to be achievable, if and only if the feedback graph is uniformly connected, plus a detectability condition. For the case when the feedback graph is directed and involves switching changes, a stronger condition than uniformly connected graph is obtained to prove the leader-following state consensus. A numerical example is worked out to illustrate our consensus results.