Leader-following consensus of linear time-varying multi-agent systems under fixed and switching topologies.

The leader-following consensus problems for linear time-varying multi-agent systems under fixed and switching topologies are considered. Several results are derived on the basis of Lyapunov’s direct method. For a network of linear time-varying agents with fixed topology, we provide two protocols, respectively. One of them uses global information of the communication topology. It guarantees the multi-agent system to go to the leader-following agreement with an arbitrarily given exponential rate. The other uses local information associated with each follower, and is implemented in a fully distributed fashion. It has robustness with respect to a certain degree of link failure. It is extended to a network of linear time-varying agents with switching topology. The resulting protocol guarantees the multi-agent system to achieve the leader-following consensus, if the union of switching graphs has a spanning tree rooted at the leader. It also has robustness with respect to a certain degree of link failure. Simulation examples are provided to validate the effectiveness of the results.