Distributed Control for Signed Networks of Nonlinear Agents

This paper copes with distributed control problems for signed networks that consist of a group of nonlinear agents. A distributed control algorithm is designed by using the nearest neighbor rule. For Lipschitz-type nonlinear dynamics, this algorithm guarantees structurally balanced signed networks to achieve bipartite consensus and structurally unbalanced signed networks to reach state stability, respectively. When bounded nonlinear dynamics are considered, all agents exponentially converge to a definite bound within a finite time, regardless of whether the signed networks are structurally balanced or structurally unbalanced. A Lyapunov approach is simultaneously exploited to carry out the dynamic behaviors analysis of signed networks. Four examples are provided to demonstrate the validity of the developed theoretical results.