Dynamic quantised feedback stabilisation of discrete-time linear system with white noise input

Abstract

In this paper, we mainly focus on the problem of quantised feedback stabilisation of a stochastic discrete-time linear system with white noise input. The dynamic quantiser is used here. The stability of the system under state quantisation and input quantisation is analysed in detail, respectively. Both the convergence of the state's mean and the boundedness of the state's covariance matrix norm should be considered when analysing its stability. It is shown that for the two situations of the state quantisation and the input quantisation, if the system without noise input can be stabilised by a linear feedback law, it must be stabilised by the dynamic quantised feedback control policy. The sufficient conditions that the dynamic quantiser should satisfy are given. Using the results obtained in this paper, one can test whether the stochastic system is stabilisable or not. Numerical examples are given to show the effectiveness of the results.

Keywords:

• stochastic system
• white noise
• dynamic quantised feedback stabilisation
• state quantisation
• input quantisation

Acknowledgements

The authors would like to thank the editors and the anonymous reviewers for their helpful comments and suggestions.

Additional information

Funding

This paper is partly supported by the National Science Foundation of China [grant number 61025016], [grant number 11072144], [grant number 61034008], [grant number 61221003].

Notes on contributors

Mingming Ji

Mingming Ji received her BS and MS degrees in applied mathematics from Northwestern Polytechnical University, Xi’an, China, in 2004 and 2007, respectively. She is now working toward a PhD degree in Department of Automation, Shanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing, Ministry of Education of China. Her current research interests include networked control systems, quantised control and their applications in industry.

Xing He

Xing He received his BS and MS degrees from Northwestern Polytechnical University, Xi’an, China in 1990 and 1993, respectively, and his PhD degree from Shanghai Jiao Tong University, Shanghai, China in 1995. Since 1995, he joined the Department of Automation, Shanghai Jiao Tong University, where he is currently an associate professor. His research interests include distributed control, robust control and networked control.

Weidong Zhang

Weidong Zhang received his BS, MS and PhD degrees from Zhejiang University, Hangzhou, China in 1990, 1993 and 1996, respectively. He worked in National Key Laboratory of Industrial Control Technology as a post-doctor before joining Shanghai Jiao Tong University, Shanghai, China, in 1998 as an associate professor. Since 1999 he has been a professor at the Department of Automation, Shanghai Jiao Tong University. He served as the Deputy Dean of the Department of Automation, Shanghai Jiao Tong University. He has authored or coauthored over 200 journal and conference papers. His research interests include robust control, distributed control and their applications in industry.