Consensus of nonlinear multi-agent systems with directed switching graphs: A directed spanning tree based error system approach

The leaderless consensus problem of multi-agent systems with nonlinear dynamics and directed switching communication graphs is considered in this paper. The assumption in previous work that each possible communication graph contains a directed spanning tree is relaxed in this paper. Based on the directed spanning tree, we propose an error system which well transforms the consensus problem into the stabilization problem. By using matrix analysis theory and stability analysis of the nonlinear systems, a new kind of multiple Lyapunov function which depends on the communication graphs, is designed for analyzing the consensus behavior of the system. It is theoretically shown that the consensus can be achieved if the coupling gain is carefully chosen and other threshold conditions based on the communication graphs are satisfied. Finally, an example is presented to illustrate the theoretical analysis.