Bipartite consensus problems of Lurie multi-agent systems over signed graphs: A contraction approach

Abstract

This paper examines the bipartite consensus problems for the nonlinear multi-agent systems in Lurie dynamics form with cooperative and competitive communication between different agents. Based on the contraction theory, some new conditions for the nonlinear Lurie multi-agent systems reaching bipartite leaderless consensus and bipartite tracking consensus are presented, respectively. Compared with the traditional methods, this approach degrades the dimensions of the conditions, eliminates some restrictions of the system matrix and extends the range of the nonlinear function. Finally, two numerical examples are provided to illustrate the efficiency of our results.