Global $H_\infty$ Consensus of Multi-Agent Systems with Lipschitz Nonlinear Dynamics

Abstract: This paper addresses the global consensus problems of a class of nonlinear multi-agent systems with Lipschitz nonlinearity and directed communication graphs, by using a distributed consensus protocol based on the relative states of neighboring 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 which can achieve global consensus with a guaranteed $H_\infty$ performance for a Lipschitz multiagent 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.