Controllability on a class of switched time-varying systems with impulses and multiple time delays

Abstract

The problem of complete controllability is addressed for a class of switched time-varying impulsive systems under multiple input delays. Several controllability criteria are obtained with the aid of algebraic and geometric tools. Firstly, the explicit expression of solution on every impulsive interval for such systems is derived by mathematical induction and variation of parameters. Then, complete controllability is investigated for the underlying system based on the solution established. Specifically, the new necessary or/and sufficient algebraic controllability conditions are obtained without assuming that all impulse-dependent matrices are non-singular. In addition, the geometric criteria with regard to the constant matrices are further discussed when the considered system reduces to a time-invariant case. Finally, numerical examples are worked out to demonstrate the controllability tests derived in this paper. It is shown that the existence of the delayed term will potentially affect the controllability of the studied system. In contrast to the existing literatures, the criteria derived in this paper removing some constrained assumptions have less conservatism and can be used to verify the controllability of a more general linear hybrid system.

Keywords:

• Complete controllability
• switched system
• impulsive effect
• delayed input
• multiple time delays

Data availability statement

Data sharing is not applicable to this article as no new data were created or analysed in this study.

Disclosure statement

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

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China [Grant Numbers 61772086, 61633011, 61976100 and 61976099].

Notes on contributors

Ding-Xue Zhang

Ding-Xue Zhang received the B.Sc. and M.Sc. degrees in petroleum engineering from the Jianghan Petroleum Institute, Jingzhou, China, in 1998 and 2003, respectively, the Ph.D. degree in control engineering from the Huazhong University of Science and Technology, Wuhan, China, in 2007. He is currently an Associate Professor with Yangtze University. His current research interests include multi-agent networks, oil production systems, and complex networks.

Jiayuan Yan

Jiayuan Yan is currently working toward the Ph.D. degree at Huazhong University of Science and Technology, Wuhan, China. His research interests include impulsive and hybrid control systems, multi-agent networks, controllability, and observability.

Bin Hu

Bin Hu received the Ph.D. degree in control science and engineering from the Huazhong University of Science and Technology (HUST), Wuhan, China, in 2015. She is currently an Associate Professor with the School of Artificial Intelligence and Automation, HUST. Her current research interests include hybrid dynamical systems, complex networks, computational neuroscience, and artificial intelligence.

Zhi-Hong Guan

Zhi-Hong Guan received the Ph.D. degree in automatic control theory and applications from the South China University of Technology, Guangzhou, China, in 1994. In 1994, he was a Full Professor with the Jianghan Petroleum Institute, Jingzhou, China. Since 1997, he has been a Full Professor with the Huazhong University of Science and Technology, Wuhan, China, where he has been a Huazhong Leading Professor since 2011. His research interests include complex systems and complex networks, impulsive and hybrid control systems, networked control systems, multi-agent systems, networked robotic systems, neural networks, and artificial intelligence. He was awarded the Natural Science Award (First Class) from the Ministry of Education of China in 2005 and the Natural Science Award (First Class) from the Hubei Province of China in 2014. He is a Highly Cited Researcher in Control and Systems Engineering (Elsevier).

Ding-Fu Zheng

Ding-Fu Zheng is a Lecturer in the School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan, China. He is pursuing a Ph.D. degree in the School of Artificial Intelligence and Automation, Huazhong University of Science and Technology. His research interests include intelligent robot, process control, and complex systems integration.