Bipartite consensus for nonlinear time-delay multiagent systems via time-varying gain control method

The bipartite consensus problem is addressed for a class of nonlinear time-delay multiagent systems in this paper. Therein, the uncertain nonlinear dynamics of all agents satisfy a Lipschitz growth condition with unknown constants, and part of the state information cannot be measured. In this case, a time-varying gain compensator is constructed, which only utilizes the output information of the follower and its neighbors. Subsequently, a distributed output feedback control protocol is proposed on the basis of the compensator. According to Lyapunov stability theory, it is proved that the bipartite consensus can be guaranteed by means of the designed control protocol. Different from the existing literature, this paper studies the leader–follower consensus problem under a weaker connectivity condition, i.e., the signed directed graph is structurally balanced and contains a directed spanning tree. Two simulation examples are carried out to show the feasibility of the proposed control strategy.