Containment in leader–follower networks with switching communication topologies

We study bipartite, first-order networks where the nodes take on leader or follower roles. Specifically, we let the leaders’ positions be static and assume that leaders and followers communicate via an undirected switching graph topology. This assumption is inspired by the swarming behavior of silkworm moths, where female moths intermittently release pheromones to be detected by the males. The main result presented here states that if the followers execute the linear agreement protocol, they will converge to the convex hull spanned by the leaders’ positions as long as the time-varying undirected graph defining the communication among all agents is jointly connected. The novelty of this research is that we use LaSalle’s Invariance Principle for switched systems, and additionally, the result is shown to hold for arbitrary state dimensions.