pth moment polynomial input-to-state stability of switched neutral pantograph stochastic hybrid systems with Lévy noise

Abstract

This article discusses pth ($p\ge 1$) moment polynomial integral input-to-state stability (iISS) and $(t+1{)}^{{\theta }_0}$-weighted integral input-to-state stability ($(t+1{)}^{{\theta }_0}$-weighted iISS) of the switched neutral pantograph stochastic hybrid systems with Lévy noise (SNPSHSs-LN) provided that all dynamical subsystems are input-to-state stability (ISS). Under the linear growth hypothesis, the criteria of ISS-type characterisation are deduced by using random analysis techniques, Lyapunov stability theory and some useful inequality techniques on the basis of the dynamic conditions of the system itself, which is an improvement on existing results about neutral systems. Finally, the theoretical results are demonstrated with a numerical example.

Keywords:

• Input-to-state stability
• Lévy noise
• pantograph delay
• linear growth hypothesis
• Lyapunov stability theory

Acknowledgements

The authors would like to thank the reviewer for their detailed comments and helpful advice.

Data availability statement

The data that support the findings of this study are available from the corresponding author Feiqi Deng, upon reasonable request.

Disclosure statement

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

Additional information

Funding

This work was supported by the National Natural Science Foundation of China Under Grants 62073144, 61873099, the Natural Science Foundation of Guangdong Province Under Grant 2020A1515010441 and Guangzhou Science and Technology Planning Project Under Grants 202002030389, 202002030158.

Notes on contributors

Peilin Yu

Peilin Yu received the B.S. degree from Huaibei Normal University, Huaibei, China, in 2017 and the M. S. degree from Anhui University, Hefei, China, in 2020. She is now a Ph.D. candidate of South China University of Technology, Guangzhou, China. Her research interests include neural networks, stochastic systems, stability analysis, and robust control theory of complex systems.

Feiqi Deng

Feiqi Deng received the Ph.D. degree in control theory and control engineering from South China University of Technology, Guangzhou, in 1997. Since October 1999, he has been a Professor with the South China University of Technology and the Director of the Systems Engineering Institute. He is currently a Member of Technical Committee on Control Theory (TCCT), Chinese Association of Automation, and now he is serving as the chair of the IEEE SMC Guangzhou Chapter and the Director of Sub-committee on Stochastic Systems Control of TCCT, a Vice Editor-in-Chief of Journal of South China University of Technology, and members of the editorial boards of the following journals: Control Theory and Applications, Journal of Systems Engineering and Electronics, and Journal of Systems Engineering, etc.. His main research interests include stability, stabilisation, and robust control theory of complex systems, including time-delay systems, nonlinear systems and stochastic systems. He is now a senior member of the IEEE.

Fangzhe Wan

Fangzhe Wan was born in 1994. He received the M.S. degree in school of sciences, Nanchang University, Nanchang, China, in 2020. He is currently pursuing the Ph.D. degree in control science and engineering with the South China University of Technology, Guangzhou, China. His current research interests include stability of neutral stochastic systems, hybrid nonlinear stochastic systems, and stochastic control systems. E-mail: [email protected].

Xiongding Liu

Xiongding Liu (Student Member, IEEE) received the M.S. degree in school of electronic and information from Yangtze University, Jingzhou, China, in 2020. He is currently pursuing the Ph.D. degree in control science and engineering with the South China University of Technology, Guangzhou, China. His current research interests include stochastic control systems, multi-agent systems and networked control systems.