Leaderless consensus of multi-agent systems with Lipschitz nonlinear dynamics and switching topologies

This paper considers the leaderless consensus problem of multi-agent systems with Lipschitz nonlinearities. The communication topology is assumed to be directed and switching. Based on the property that the graph Laplacian matrix can be factored into the product of two specific matrices, the consensus problem with switching topologies is converted into a stabilization problem of a switched system with lower dimensions by performing a proper variable transformation. Then the consensus problems are solved with two different topology conditions. Firstly, with the assumption that each possible topology contains a directed spanning tree, the consensus problem is solved using the tools from stability analysis of slow switching systems. It is proved that the leaderless consensus can be achieved if the feedback gains matrix is properly designed and the average dwell time larger than a threshold. Secondly, by using common Lyapunov function based method, the consensus problem with arbitrary switching topologies is solved when each possible topology is assumed to be strongly connected and balanced. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.