Abstract: This paper is devoted to investigate the consensus problems for the multi-agent systems with Lurie nonlinear dynamics in directed topology. Under some assumptions, some sufficient conditions for the systems reaching leaderless consensus and tracking consensus are established by using contraction analysis theory. Compared with the existing results, there is no need to formulate the multi-agent networks in compact form. These conditions are only related to the individual agent in lower-dimensional case and the communication topology of the network. Additionally, a generalized nonlinear function is introduced. Finally, three numerical examples are demonstrated to illustrate the effectiveness of the theoretical results.

Key words: contraction theory, virtual system, partial contraction theory, Lurie dynamics, nonlinear multi-agent systems