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H ∞ bipartite consensus of nonlinear multi-agent systems over a directed signed graph with a leader of non-zero input

This paper examines the bipartite tracking consensus for nonlinear multi-agents over a directed signed graph under bounded disturbances and a non-zero bounded input of the leader. For dealing with disturbances, the 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 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, 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.