Bipartite coordination for the Structurally Balanced Networks

Under the signed graph, the bipartite containment control problem is studied for the linear multi-agent systems. Since structurally balanced is one of the characteristics of signed graph, M-matrix given in many articles on containment control does not apply to this paper. Thus, a concise and novel method is presented to solved such problem. A novel definition about bipartite containment is given to show that agents in different groups will reach different coordination, respectively. A distributed bipartite observer is proposed to estimate the state of the convex hull. Then, a distributed state feedback control protocol is designed to solve the main problem of this paper. Finally, a numerical example is given to illustrate the validity of the theoretical results.