Forced consensus in networks of double integrator systems with delayed input

This communique presents forced second-order consensus protocols with communication time-delays for the network of agents with double integrator dynamics and gives a measure of the robustness of the protocols to the communication time-delays. By employing a frequency domain method, it is proven that the forced consensus is achieved asymptotically for appropriate time-delay if the network is connected. Particularly, the maximum fixed time-delay that can be tolerated by the network is found. The forced consensus protocols are distributed in the sense that each agent only needs information from its neighboring agents, which reduces the complexity of connections between agents significantly. Numerical simulation results are provided to demonstrate the effectiveness and the sharpness of the theoretical results.