Multi-leader set coordination of multi-agent systems with random switching topologies

In this paper, we consider the multi-leader following problem of a second-order multi-agent system with random switching topologies. This problem can also be viewed as a tracking problem of a target set specified multiple leaders. The interaction topology between agents is described by an irreducible Markov chain. A necessary and sufficient condition is obtained to make all the mobile agents almost surely asymptotically converge to the static convex target set determined by multiple leaders. Moreover, results are also given for the moving target set with independent and identically distributed (i.i.d.) random switching, too.