Consensus of Lur'e-type nonlinear multi-agent systems with a class of directed switching topologies

This paper addresses the consensus problem of Lur'e-type nonlinear multi-agent systems with directed switching topologies. A special class of directed topologies containing a directed spanning tree is characterized. Distributed consensus controllers are constructed based on relative states information of neighbor agents. A special property of the graph Laplacian matrix is used to convert the consensus problem with switching topologies into a stabilization problem of a switched system with lower dimensions. Common Lyapunov function based approach is employed for analysis. A bright feature of this paper is that the consensus of Lur'e-type nonlinear multi-agent systems can be achieved with directed and arbitrarily fast switching topologies. There is also no any constrains on the dwell time or the averaging dwell time of the switching topologies. Finally, a numerical simulation is provided to illustrate the effectiveness of the theoretical results.