Bipartite containment tracking of signed networks

This paper considers a class of bipartite containment tracking problems for leader-following networks associated with signed digraphs. It admits multiple leaders which can be not only stationary but also dynamically changing via interactions between them and their neighbored leaders. It is shown that the followers can converge to the convex hull containing each leader's trajectory as well as its symmetric trajectory which is the same as it in modulus but different in sign. In particular, if the adjacency weight matrix of the digraph is not signed but nonnegative, then the leader-following network achieves the traditional containment tracking. Simulation tests are performed to illustrate the observed bipartite containment tracking performances of signed networks.