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In this paper, a cooperation network and a competition network consensus problem of multi-agent systems is study. The communication topology among agent is characterized by a directed and connected graph. And Communication between the cooperation network and the competition network through their respective leaders. The two networks can be made to reach stable and consensus by setting parameters and between the two leaders. Sufficient conditions are derived to reach a global consensus based on algebraic graph , matrix theory, and stability theory. With theoretical analysis, it obtains the value range of the parameters. For the case of switching topology, a sufficient condition is obtained under the assumption that the total period over which the leader is globally reachable is sufficiently large. Finally, through the MATLAB simulation, an example is presented to illustrate the correctness of the theoretical results.

Consensus of Two Leader-Following Multi-agent Systems between the Cooperation Network and the Competition Network