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This study addresses the global consensus problems of a class of non-linear multi-agent systems with Lipschitz non-linearity and directed communication graphs, by using a distributed consensus protocol based on the relative states of neighbouring agents. A two-step algorithm is presented to construct a protocol, under which a Lipschitz multi-agent system without disturbances can reach global consensus for a strongly connected directed communication graph. Another algorithm is then given to design a protocol that can achieve global consensus with a guaranteed H∞ performance for a Lipschitz multi-agent system subject to external disturbances. The case with a leader-follower communication graph is also discussed. Finally, the effectiveness of the theoretical results is demonstrated through a network of single-link manipulators.