Second-order consensus protocol design in multi-agent systems: A general framework

In this paper, a second-order consensus protocol is designed in multi-agent systems. A general model of multi-agent systems with second-order dynamics is proposed, where for each agent, the second-order dynamics depend on the position, velocity, and decays of both position and velocity of agents. First, a necessary and sufficient condition is provided which ensures second-order consensus of multi-agent systems. It is found that both the real and imaginary parts of eigenvalues of Laplacian matrix are very important. Second, five specific different situations are analyzed and compared with each other. Finally, some simulation examples are provided to verify the theoretical analysis of this paper.