Swarm stability for high-order linear time-invariant singular multi-agent systems

Abstract

Swarm-stability and swarm-stabilisation problems for high-order linear time-invariant singular multi-agent systems with directed networks are investigated. First, necessary and sufficient conditions for swarm stability and asymptotic swarm stability are proposed, which are independent of the dimensions of Jordan blocks of the Laplacian matrix of the interaction topology. Then, an approach is given to determine the absolute motion as a whole, and it is shown that the absolute motion is completely determined by initial states if the interaction topology is balanced. Furthermore, an approach is presented to determine gain matrices for asymptotic swarm stabilisation. Moreover, leader-following swarm-stability and swarm-stabilisation problems are investigated. Finally, numerical examples are given to demonstrate theoretical results.

Keywords:

• singular multi-agent system
• swarm stability
• asymptotic swarm stabilisation
• high order

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grants 61174067 and 61263002.

Additional information

Notes on contributors

Jianxiang Xi

Jianxiang Xi was born in 1982. He received his BS and MS degrees from the High-Tech Institute of Xi'an, Xi'an, China, in 2004 and 2007, respectively. He received his PhD degree in control science and engendering from the High-Tech Institute of Xi'an, Xi'an, China, in 2012 by a coalition formed with Tsinghua University. He is currently a lecturer in control science and engendering at the High-Tech Institute of Xi'an. His research interests include complex systems control, switched systems and swarm systems.

Zhicheng Yao

Zhicheng Yao was born in 1975. He received his BS and MS degrees from the High-Tech Institute of Xi'an, Xi'an, China, in 1996 and 2003, respectively. He is currently a associate professor in control science and engendering at the High-Tech Institute of Xi'an. His research interests include Global Navigation Satellite Systems (GNSS) signal processing and swarm systems.

Guangbin Liu

Guangbin Liu was born in 1963. He received his BS degree from the High-Tech Institute of Xi'an, Xi'an, China, in 1984, and his MS and PhD degrees from Xi'an Jiaotong University, Xi'an, China, in 1989 and 1993, respectively. He is currently a professor in control science and engendering at the High-Tech Institute of Xi'an. His research interests include Global Navigation Satellite Systems (GNSS) signal processing, complex systems control and swarm systems.

Yisheng Zhong

Yisheng Zhong received his BE degree in control engineering from the Harbin Institute of Technology, Harbin, China, in 1982, the ME degree in electronic engineering from the University of Electro-Communications, Tokyo, Japan, in 1985, and the PhD degree in electrical engineering from Hokkaido University, Sapporo, Japan, in 1988. He was a postdoctorate scholar at Tsinghua University, Beijing, China, from 1989 to 1990, and since 1991, he has been with the Department of Automation, Tsinghua University, where he is currently a professor and also with the Tsinghua National Laboratory for Information Science and Technology. His research interests include robust control, nonlinear control and electromechanical system control.