Non-smooth Lyapunov function for nonlinear consensus problem

Consensus of multi-agent systems (MAS) is an intriguing topic recent years due to its widely application in robotics, biology, computer and social science. Traditionally, construction of smooth Lyapunov function can be viewed as an effective method for the stability analysis of MAS with fixed topology. On one hand, the evolution of MAS is inevitably involved in dynamical environments and the recent development of MAS requires systematic tools for the analysis of MAS with dynamic topology. On the other hand, the interactions between agents are more likely to be nonlinear in the real world and the investigation of MAS has not too much concern on nonlinear models yet. Facing these problems, this paper takes a non-smooth Lyapunov candidate to investigate the consensus of a representative nonlinear MAS with dynamical topology. Several consensus criteria are proposed and simulation results validate the effectiveness of these criteria.