Delayed-state-derivative feedback for improving consensus performance of second-order delayed multi-agent systems

Abstract

In this article, delayed-state-derivative feedback is introduced into the existing delayed consensus protocol for improving the robustness against communication delay and the convergence speed of reaching the consensus simultaneously. Frequency-domain analysis and algebra graph theory are employed to derive the sufficient and necessary condition guaranteeing the second-order delayed multi-agent system applying the consensus protocol with the delayed-state-derivative feedback to achieve the stationary consensus asymptotically. It is proved that introducing delayed-state-derivative feedback with the proper intensity can improve the robustness against communication delay and that for two particular kinds of second-order delayed multi-agent systems, introducing the delayed-state-derivative feedback can also accelerate the convergence speed, provided that the intensity of the delayed-state-derivative feedback is chosen properly. Simulations are provided to demonstrate the effectiveness of the theoretical results.

Keywords:

• multi-agent systems
• delayed-state-derivative feedback
• consensus
• communication delay
• robustness
• convergence speed

Acknowledgements

This work was supported by the National Natural Science Foundation of China under grants 60574088 and 60874053.