Bipartite Consensus for a Class of Second-order Nonlinear Multi-agent Systems

This paper focuses on the problem of second-order bipartite consensus in nonlinear multi-agent systems concerning leader-following. A novel definition of the Lipschitz condition is proposed to solve the nonlinear term in the leader following the bipartite consensus problem. In addition, a procedure for adaptive output feedback control is proposed, which can continuously adjust the output of the controller to achieve stability. By utilizing the linear matrix inequality technique, a sufficient condition is proposed to ensure that the considered nonlinear multi-agent systems implement leader-following bipartite consensus. Finally, the validity and feasibility of the theoretical result are demonstrated through numerical simulations.