Event-triggered polynomial input-to-state stability in mean square for pantograph stochastic systems

Abstract

This article investigates the polynomial integral input-to-state stability in mean square (ms-PIISS) and polynomial $(t+1{)}^{\mathrm{\aleph }}$-weighted integral input-to-state stability in mean square ($(t+1{)}^{\mathrm{\aleph }}$-weighted ms-PIISS) for pantograph stochastic systems. The above stability is achieved through dynamic event-triggered mechanism and static event-triggered mechanism. To avert Zeno behaviour in each sample path, our event-triggered mechanisms (ETMs) force a pause time after each successful execution, which will lead to intermittent detection of system status, thus greatly saving communication resources. One utilises the Hanalay-type inequality to obtain the less conservative stability criterion. In addition, a collaborative design method of ETM and linear controller is proposed. Ultimately, an paraphrastic example is shown to indicate the availability of the mentioned collaborative design process.

Keywords:

• Pantograph stochastic systems
• Input-to-state stability
• Dynamic event-triggered mechanism
• Static event-triggered mechanism

Disclosure statement

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

Data availability statement

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

Additional information

Funding

This work was supported in part by the China Scholarship Council Scholarship [grant number CSC202206150105], in part by the National Natural Science Foundation of China [grant numbers 62073144, 62273157, 11771001], in part by NSERC Canada, in part by the Guangdong Basic and Applied Basic Research Foundation [grant number 2023B1515020091].

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.

Xinzhi Liu

Xinzhi Liu received the B.Sc. degree in mathematics from Shandong Normal University, Jinan, China, in 1982, and the M.Sc. and Ph.D. degrees in applied mathematics from the University of Texas at Arlington, Arlington, TX, USA, in 1987 and 1988, respectively. He spent two years as a Postdoctoral Fellow with the University of Alberta, Edmonton, AB, Canada, and then joined the Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada, as an Assistant Professor in 1990, where he became an Associate Professor in 1994 and a Full Professor in 1997. He is the author or co-author of over 400 research articles, six research monographs, and 20 edited books. His current research interests include hybrid dynamical systems, stability and control, multi-agent systems and complex networks, infectious disease modelling, and communication security.

Yuanyuan Sun

Yuanyuan Sun was born in Anshan, Liaoning, China, in 1996. She is currently pursuing the Ph.D. degree in control science and engineering with the School of Automation Science and Engineering, South China University of Technology, Guangzhou, China. Her current research interests include the stochastic systems and quantised control.