Finite-time boundedness of Markovain jump nonlinear systems with incomplete information

ABSTRACT

This paper deals with the finite-time $H_{\mathrm{\infty }}$ bounded control problem of a class of uncertain Markovian jump nonlinear systems with partially unknown transition probabilities and norm-bounded disturbances. The purpose of the paper is to derive a stochastic finite-time controller such that the resulting nominal or uncertain stochastic nonlinear model is stochastically finite-time $H_{\mathrm{\infty }}$ bounded by applying stochastic analysis techniques and free connection weighting matrix approach. We also provide stochastic finite-time stability and stochastic finite-time boundedness criteria of the class of nominal or uncertain stochastic nonlinear dynamics. Moreover, the derived criteria can be simplified into linear matrix inequalities (LMIs), which could be solved by employing Matlab LMI toolbox. Finally, the effectiveness of proposed approaches is demonstrated by a practical example.

KEYWORDS:

• Markovian jump nonlinear systems
• stochastic finite-time boundedness
• stochastic finite-time $H_{\mathrm{\infty }}$ boundedness
• incomplete transition probabilities

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Yingqi Zhang http://orcid.org/0000-0001-7338-949X

Jeng-Shyang Pan http://orcid.org/0000-0002-2354-5834

Additional information

Funding

Supported by Foundation of Henan Educational Committee (18A110001), Key Laboratory of Grain Information Processing and Control (Henan University of Technology) of Ministry of Education (KFJJ2016111), and National Natural Science Foundation of China (NNSFC) (U1509217).

Notes on contributors

Yingqi Zhang

Yingqi Zhang received the Ph.D. degree from the Department of Mathematics, Zhengzhou University of China, Zhengzhou, Henan, China, in 2009. Since 2016, he has been with the College of Science, Henan University of Technology, Zhengzhou, as a Professor. He has published over 60 refereed journal and conference papers on nonlinear control systems, robust control systems, fuzzy systems, nonlinear time-delay systems, and neural networks. He has reviewed for many Journals, such as the Automatica, the IEEE Transactions on Fuzzy Systems, the International Journal of Robust and Nonlinear Control, the Journal of the Franklin Institute, the Information Sciences, the IET Control Theory and Applications, the Applied Mathematics Letters, and so forth. His research interests include stochastic systems, fuzzy systems, singular systems, finite-time control, robust control for uncertain systems, and neural networks.

Yang Yang

Yang Yang received the B.S. degree from School of mathematics and statistics from Nanyang Normal University, China. His research interests include finite-time control, switched systems, robust control for uncertain systems and neural networks. He is currently working towards the M.S. degree with the Henan University of Technology, Zhengzhou, China.

Peng Shi

Peng Shi received the Ph.D. degree in Electrical Engineering from the University of Newcastle, Australia in 1994; the Ph.D. degree in Mathematics from the University of South Australia in 1998. He was awarded the Doctor of Science degree from the University of Glamorgan, Wales in 2006; and the Doctor of Engineering degree from the University of Adelaide, Australia in 2015. He is now a professor at the University of Adelaide. His research interests include system and control theory, intelligent systems, and operational research. He is a Member-at-Large of Board of Governors, IEEE SMC Society, and an IEEE Distinguished Lecturer. He is a Fellow of the Institute of Electrical and Electronic Engineers, the Institution of Engineering and Technology, and the Institute of Engineers, Australia. He received the Andrew Sage Best Transactions Paper Award from IEEE SMC Society in 2016. He has served on the editorial board of a number of journals in the fields of automation, fuzzy systems, cybernetics, signal processing and information sciences.

Jeng-Shyang Pan

Jeng-Shyang Pan received the B.S. degree in Electronic Engineering from the National Taiwan University of Science and Technology in 1986, the M.S. degree in Communication Engineering from the National Chiao Tung University, Taiwan in 1988, and the Ph.D. degree in Electrical Engineering from the University of Edinburgh, U.K. in 1996. Currently, he is a Dean for College of Information Science and Engineering, Fujian University of Technology and a director of Innovative Information Industry Research Center, Harbin Institute of Technology Shenzhen Graduate School, China. He joined the editorial board of LNCS Transactions on Data Hiding and Multimedia Security, Journal of Computers, Journal of Information Hiding and Multimedia Signal Processing, etc. His current research interests include soft computing, information security and signal processing.