Stabilisability of discrete-time multi-agent systems under fixed and switching topologies

ABSTRACT

This paper studies the problem of stabilisability for general discrete-time linear multi-agent systems. For fixed topology, a necessary and sufficient graph-theoretic condition is proposed. Based on this, a general linear form of the external control input is given, and two methods to design the feedback gain matrix by Riccati equality/inequality are given. For switching topology, a sufficient graph-theoretic condition is presented, under which the stabilisability of multi-agent systems is achieved by introducing an averaging analysis approach. Additionally, both results under fixed and switching topologies are applied for solving the tracking and formation control of discrete-time multi-agent systems, and some sufficient and/or necessary conditions are presented. Finally, numerical examples are given to illustrate the theoretical results.

KEYWORDS:

• Multi-agent systems
• stabilisability
• discrete-time
• switching topology

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Yongqiang Guan http://orcid.org/0000-0001-5580-1284

Additional information

Funding

This work is supported by National Science Foundation of China [grant numbers 61603288, 61773023] and the Fundamental Research Funds for the Central Universities [grant numbers JBX170408, JBX180401].

Notes on contributors

Yongqiang Guan

Yongqiang Guan received his Ph.D. degree in control science and engineering from Beihang University, Beijing, China, in 2016. From July 2015 to May 2016, he served as a Research Assistant at the department of Mechanical Engineering, University of Hong Kong. He is currently a lecturer at the School of Mechano-electronic Engineering, Xidian University, Xi’an, China. His current research interests include coordination of multi-agent systems, complex networks and collective intelligence.

Xianglei Kong

Xianglei Kong received the B.S. and the M.Eng. degrees in mathematics and control science and engineering from Xidian University, Xi’an, China, in 2015 and 2018, respectively. She is currently a software engineer at BAIDU. She current research interests include multi-agent systems and control, intelligent optimize algorithm.