Linear and nonlinear generalized consensuses of multi-agent systems

Consensus in directed networks of multiple agents, as an important topic, has become an active research subject.Over the past several years, some types of consensus problems have been studied. In this paper, we propose a novel type of consensus, the generalized consensus(GC), which includes the traditional consensus, the anti-consensus, and the cluster consensus as its special cases. Based on the Lyapunov's direct method and the graph theory, a simple control algorithm is designed to achieve the generalized consensus in a network of agents. Numerical simulations of linear and nonlinear GC are used to verify the effectiveness of the theoretical analysis.