On Convergence Rate of Leader-Following Consensus of Linear Multi-Agent Systems With Communication Noises

• Published in: IEEE transactions on automatic control Vol. 61; no. 11; pp. 3586 - 3592
• Main Authors: Cheng, Long, Wang, Yunpen, Ren, Wei, Hou, Zeng-Guang, Tan, Min
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.11.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Asymptotic properties; Attenuation; Automatic control; Convergence; Convergence rate; Gain; leader-following consensus; Mean square values; Multi-agent systems; Multiagent systems; Noise; noises; Protocols; Switches; Time-domain analysis; time-varying gain; Topology; Transient analysis
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2016.2522647

This note further studies the previously proposed consensus protocol for linear multi-agent systems with communication noises. Each agent is allowed to have its own time-varying gain to attenuate the effect of communication noises. Therefore, the common assumption that all agents have the same noise-attenuation gain is not necessary. It has been proved that if all noise-attenuation gains are infinitesimal of the same order, then the mean square leader-following consensus can be reached. Furthermore, the convergence rate of the multi-agent system has been investigated. If the noise-attenuation gains belong to a class of functions which are bounded above and below by t -β (β ∈ (0, 1)) asymptotically, then the second-moment of the relative state between each follower agent and the leader agent is characterized by a function bounded above by t -β asymptotically.