Global consensus regions of multi-agent systems with nonlinear dynamics

This paper addresses the global consensus problem of multi-agent systems with a leader-follower communication topology consisting of Lur´e type of node dynamics. A decomposition approach is proposed to convert the consensus of a high-dimensional Lur´e network into the test of a set of matrix inequalities whose dimensions are the same as a single node system. The notion of global consensus region is then introduced and analyzed. A necessary and sufficient condition is derived for the existence of a consensus protocol to guarantee a desirable unbounded consensus region. A multi-step design procedure is given for constructing such a consensus protocol, which maintains a favorable decoupling property. The effectiveness of the theoretical results is demonstrated through a network of Chua´s circuits.