New Conditions for Consensus of Second-Order Multi-agent Systems

This note studies the consensus problems of second-order multi-agent systems in terms of the system parameters, including the inertia, the velocity damping and the coupling strength. Based on matrix theories, the convergence conditions for two kinds of multi-agent systems to reach consensus are respectively derived. The conditions indicate that the network structure of multi-agent systems can be optimized by adjusting the system parameters. Under these conditions, the second-order multi-agent systems have the similar properties to the first-order multi-agent systems that increasing the coupling strength of relative positions, or relative velocities between neighboring agents can improve the convergence rate when the directed graph has a directed spanning tree. The results may serve as a mechanism for designing networked systems for the sake of improving the convergence rate and reducing the consumption of energy.