Global consensus control of Lipschitz nonlinear multi-agent systems

This paper addresses the distributed global consensus problem of a class of nonlinear multi-agent systems with Lipschitz nonlinearity. A distributed consensus protocol based on the relative states of neighboring agents is proposed. The global consensus problem of a Lipschitz nonlinear multi-agent system is cast into the feasibility of a set of matrix inequalities having the same dimension as that of a single agent. The notion of global consensus region is then introduced and analyzed. It is pointed out through numerical examples that the global consensus region can serve as a measure for the robustness of consensus with respect to the communication topology. A necessary and sufficient condition for the existence of a protocol having an unbounded global consensus region is derived. A two-step procedure is further presented for constructing such a protocol. The effectiveness of the theoretical results is demonstrated through a network of single-link manipulators.