Static Bipartite Consensus Problems of Heterogeneous Signed Networks

Abstract

This paper aims to study the distributed control problems of heterogeneous signed networks whose communication topologies are undirected. A distributed control protocol is designed based on neighboring state information. With this protocol be employed, the convergence results of the heterogeneous signed network are provided. It is shown that the heterogeneous signed network can achieve the static bipartite consensus (respectively, state stability) if and only if the signed graph is structurally balanced (respectively, unbalanced). The associated convergence analyses can be developed by constructing a suitable Lyapunov function. In addition, two simulation examples are presented to validate the correctness of the obtained results.