Delay-dependent consensus condition for a class of fractional-order linear multi-agent systems with input time-delay

Abstract

The consensus problem of a class of fractional-order linear multi-agent systems with distributed control containing input time-delay is investigated. By adopting the frequency domain analysis and generalised Nyquist criterion for the fractional-order time-delay systems, the delay-dependent consensus condition is obtained. Then, we are interested in finding the maximum time-delay tolerance and give an exact formula for calculating the maximum time-delay to maintain the system is consensusable. As illustrated by the numerical examples, the proposed theoretical results work effectively and accurately.

Keywords:

• Consensus
• multi-agent system
• fractional-order linear system
• input time-delay

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Min Shi  http://orcid.org/0000-0003-3063-287X

Additional information

Funding

The authors thank the financial support of NSF of China under [grant numbers 11402125, 11602035], NSF of Jiangsu Province of China under [grant number BK20140861], NSF of Jiangsu Higher Education Institutions of China under [grant number 14KJB130003] and Nanjing University of Posts and Telecommunications Talent Introduction Foundation under [grant number NY213107].

Notes on contributors

Min Shi

Min Shi received the Ph.D. degree from the State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2013. He is currently a lecturer with the college of automation, Nanjing University of Posts and Telecommunications, Nanjing, China. His research interests include fractional-order control systems, dynamics of fractional-order systems in engineering.

Yajuan Yu

Yajuan Yu received the Ph.D. degree from the State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2017. She is currently a lecturer with the School of Mathematics and Physics, Changzhou University, Changzhou, China. Her research interests include fractional-order circuit systems, fractional-order dynamics and control systems, and time delay systems.

Qi Xu

Qi Xu received the Ph.D. degree from the State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2016. He is currently a lecturer with the School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, China. His research interests include fractional-order dynamical systems, time-delay systems.