Stabilisation of a class of positive switched nonlinear systems under asynchronous switching

ABSTRACT

This paper addresses the stabilisation problem for a class of positive switched nonlinear systems under asynchronous switching, which means that the switches between the candidate controllers and the system modes are not synchronous. The continuous and discrete cases are considered respectively. Sufficient conditions are firstly provided for the existence of the asynchronous switching controllers to guarantee the closed-loop system to be positive and exponentially stable, and the corresponding admissible switching signals are presented. As a special case, the stabilisation results for positive switched linear systems under asynchronous switching are provided accordingly. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.

KEYWORDS:

• Positive systems
• switched systems
• nonlinear systems
• stabilisation
• asynchronous switching
• average dwell time

Acknowledgements

This work was supported by the Postgraduate Innovation Project of Jiangsu Province under grant number KYLX-0371 and the National Natural Science Foundation of China under grant number 61273120.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Postgraduate Innovation Project of Jiangsu Province [grant number KYLX-0371]; the National Natural Science Foundation of China [grant number 61273120].

Notes on contributors

Shuo Li

Shuo Li received her B.S. degree in automation from Hangzhou Dianzi University, Hangzhou, China, in 2012. She is currently pursuing her Ph.D. degree in Control Theory and Control Engineering at School of Automation, Nanjing University of Science and Technology, Nanjing, China. Her current research interests include positive systems, nonlinear systems, switched systems, fuzzy systems and their applications.

Zhengrong Xiang

Zhengrong Xiang received his Ph.D. degree in control theory and control engineering at Nanjing University of Science and Technology, Nanjing, China, in 1998. Since 1998, he has been faculty member and he is currently full professor at Nanjing University of Science and Technology. He was appointed as lecturer in 1998 and associate professor in 2001 at Nanjing University of Science and Technology. He is a member of the IEEE, member of the Chinese Association for Artificial Intelligence. His main research interests include switched systems, nonlinear control, robust control and networked control systems.