This paper examines the bipartite tracking consensus for nonlinear multi-agents over a directed signed graph under $L_2$ bounded disturbances and a non-zero bounded input of the leader. For dealing with disturbances, the $H_{\mathrm{\infty }}$ control theory has been adopted to develop a robust bipartite tracking consensus protocol. An additional switching control action is proposed to counteract the bounded matching input of the leader. The proposed control ensures the asymptotic convergence of the consensus error for known matching bounded input at the leader without disturbances, and an $H_{\mathrm{\infty }}$ performance criterion from bounded disturbances to the consensus error has been provided. Contrary to the traditional consensus frameworks, our approach considers the nonlinear agents to resolve the bipartite consensus, $L_2$ disturbances for a robust distributed control, directed signed graphs, and bounded non-zero input at the leader for dealing with a realistic consensus scenario. Two simulation examples are provided for illustration.

本文研究了非线性多智能体在有向符号图上的二分跟踪一致性${\mathrm{大号}}_2$有界干扰和领导者的非零有界输入。为了处理干扰，$H_{\mathrm{\infty }}$控制理论已被用于开发稳健的二分跟踪共识协议。提出了一个额外的切换控制动作来抵消领导者的有界匹配输入。所提出的控制确保了领导者处已知匹配有界输入的共识误差的渐近收敛，并且没有干扰，并且$H_{\mathrm{\infty }}$提供了从有界干扰到共识错误的性能标准。与传统的共识框架相反，我们的方法考虑非线性代理来解决双方共识，${\mathrm{大号}}_2$鲁棒分布式控制、有向符号图和领导者有界非零输入的干扰，以处理现实的共识场景。提供了两个仿真例子来说明。