Tracking control for multi-agent consensus with an active leader and directed topology

In this paper, we consider a multi-agent consensus problem of multi-agent systems with an active leader and directed topology. The state of the considered leader not only keeps changing but also may not be measured. Two different models with and without coupling time delays are presented. In each model, two different cases of coupling topologies are investigated. A sufficient condition is proved in the case when the interconnection topology is fixed and directed. Moreover, a necessary and sufficient condition was presented when the velocity can be measured. A sufficient condition is also proposed in the case when the coupling topology is switched and balanced.