Bipartite Consensus Control of Second-Order Multiagent Systems Over Switching Networks

This paper addresses the issue of bipartite consensus control for multiagent systems. Consider that the multiagent systems have the second-order dynamics and cooperative-competitive interactions, moreover, the communication topologies among the agents are time-varying. For each agent, the consensus protocol proposed in the paper depends on the velocity information from itself and the position information from the neighboring agents. By utilizing the signed graph theory, Lyapunov function method, matrix transformation, and properties of the Kronecker product, some criteria are established for the bipartite consensus. It is demonstrated that bipartite consensus can be realized if, the gain parameter in the protocol is not less than the square root of the maximum degree of the agents, and the switching topologies are jointly connected within a time interval. Numerical simulations are provided to support the obtained theoretical results.