Finite frequency domain H_∞ consensus control of neutral multi-agent systems with input delay

Abstract

The finite frequency domain $H_{\mathrm{\infty }}$ consensus control problem of neutral multi-agent systems with the input delay is investigated in this paper for the first time. According to the linear transformation, the problem of $H_{\mathrm{\infty }}$ consensus is converted into a set of $H_{\mathrm{\infty }}$ stability problems. Through the Lyapunov theory, combined with the time-delay interval decomposition method, a less conservative controller design method for the state feedback controller is presented. And the obtained controller can ensure closed-loop multi-agent systems to fulfil the consensus. Utilizing the generalised Kalman-Yakubovich-Popov (GKYP) lemma, the sufficient condition is derived for multi-agent systems achieving the $H_{\mathrm{\infty }}$ performance in the finite frequency domain (FFD). Then, via the orthogonal spatial information of the input matrix, the conservativeness of obtained design approach is further declined. Moreover, the design method with less conservativeness is proposed for the dynamic output feedback controller. Finally, a numerical case and a multi-pendulum system controlled by the multi-motor system are presented in this paper to demonstrate the availability and applicability of the proposed methods.

Keywords:

• Linear neutral multi-agent system
• input delay
• $H_{\mathrm{\infty }}$ performance
• finite frequency domain

Data availability statement

Due to the nature of this research, participants of this study did not agree for their data to be shared publicly, so supporting data is not available.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant numbers 61004012, 61603009, 61473245].

Notes on contributors

Ao Dun

Ao Dun was born in Inner Mongolia Autonomous Region, China, in July 1978. She received the B.S. degree in electrical engineering and automation and the M.S. degree in control theory and control engineering in 2001 and 2003, respectively, and both from Yanshan University, China. She received the Ph.D. degree in general and fundamental mechanics in 2008 from the Peking University, China. She is a lecturer with the Faculty of Information Technology, Beijing University of Technology, China. Her research focuses on nonlinear system control, the multi-agent system control, the robust control and the fuzzy control.

Qianjiao Xu

Qianjiao Xu was born in Shandong Province, China, in November 1994. He received the B.S. degree in automation from Shandong University of Technology in 2017 and received the M.S. degree in control science and engineering from Beijing University of Technology in 2021, both in China. His research focuses on the multi-agent system control and finite frequency domain control.

Fei Lei

Fei Lei was born in Anhui Province, China, in August 1972. He received the Ph.D. degree in control theory and control engineering in 2005 from the Institute of Automation, Chinese Academy of Sciences, China. He is currently an associate professor with the Faculty of Information Technology, Beijing University of Technology, China. His research focuses on real-time control and pattern recognition.