Matrix-Valued Weighted Leader-Following Bipartite Consensus of Multi-Agent Systems with Switching Topology

This note studies the leader-following bipartite consensus of multi-agent systems under the matrix-valued weighted switching topology, where the speed information of the leader cannot be measured directly. Conditions are given for system to achieve bipartite consensus by using graph theory, Lyapunov stability theory and matrix theory. It can be proved that the system can achieve matrix-valued weighted leader-following bipartite consensus if leader's acceleration information is known, and the tracking error of the agents is bounded if the acceleration information is unknown. In addition, even if there exist external disturbances, we can also draw a similar conclusion. Finally, a simulation example is presented to verify the feasibility of theory.