Allowable delay bound for consensus of linear multi-agent systems with communication delay

Abstract

This paper studies the consensus of a group of linear dynamic agents with a uniform communication delay and focuses on searching an allowable delay bound. As long as the delay is less than this bound, there exist linear feedback consensus protocols driving the multi-agent system to achieve consensus. Both fixed and switching topology cases are investigated. In both cases, the consensus problem is converted to the robust stability problem of corresponding uncertain state-delayed systems. By using Lyapunov–Krasovskii functional analysis, consensus conditions which contain the feedback gain conditions and delay conditions are proposed for systems over fixed and switching topologies, respectively. Furthermore, allowable delay bounds are obtained for both systems by solving the optimal robust stabilisation problems. Numerical examples are given to illustrate the results.

Keywords:

• multi-agent systems
• consensus
• delay
• switching topology

Acknowledgements

The authors gratefully acknowledge the National Nature Science Foundation for its support under Grant Nos. 60974041, 60934006 and 61105113.

Additional information

Notes on contributors

Ya Zhang

Ya Zhang received her BS degree in Applied Mathematics from China University of Mining and Technology in 2004 and PhD degree in Control Engineering from Southeast University, China, in 2010. Since 2010, she has been with Southeast University, Nanjing, China, where she is currently a Lecturer with School of Automation. Her research interests include cooperative control and networked control systems.

Yu-Ping Tian

Yu-Ping Tian received his Bachelor degree from Tsinghua University, Beijing, China, in 1986, PhD degree from Moscow Power Institute, Moscow, USSR, in 1991 and ScD degree from Taganrog State Radio-Engineering University, Taganrog, Russia, in 1996. All his degrees are in Electrical Engineering. Since 1992, he has been with Southeast University, Nanjing, China, where he is a Professor with School of Automation. He held visiting positions with Central Queensland University, Australia, University of California at Berkeley and the City University of Hong Kong. He is the recipient of the Chang Jiang Distinguished Professorship awarded by the Education Ministry of China and the Distinguished Young Scholar Award of the National Natural Science Foundation of China. His research interests are in the fields of control theory and networking.