Finite-Time Bipartite Consensus Problems for Signed Networks With Directed Topologies

This paper concentrates on investigating the finite-time bipartite consensus problems of directed signed networks subject to both cooperative interactions and antagonistic interactions. Based on the nearest neighbor rule, a distributed control protocol is proposed to make the signed network achieve the bipartite consensus and state stability within a finite time when its associated signed digraph is structurally balanced and unbalanced, respectively. With the help of improved Lyapunov potentials, the convergence analysis can be further derived for the proposed protocol. Two simulation examples are introduced to demonstrate the effectiveness of our developed results.