Second-order consensus of multi-agent systems with time delay and heterogeneous topologies

In this paper, we propose a control algorithm to achieve consensus of multi-agent systems with time delay and heterogeneous topologies. The proposed control scheme is capable of dealing with both velocity and position time delay. The stability analysis is conducted based on Lyapunov method and graph theory and provides the proof that consensus of multi-agent systems can be achieve if the time delay is sufficiently small. Simulation results confirm our claims that positions and velocities of all agents can achieve consensus under the proposed control laws.