Sliding mode control for Markov jump linear uncertain systems with partly unknown transition rates

Abstract

In this paper, based on sliding mode control approach, the robust stabilisation problem for a class of continuous-time Markovian jump linear uncertain systems with partly unknown transition rates is investigated. The transition rate matrix under consideration covers completely known, boundary known and completely unknown elements. By making use of linear matrix inequalities technique, sufficient conditions are presented to derive the linear switching surface and guarantee the stochastic stability of sliding mode dynamics. Then a sliding mode control law is designed to drive the state trajectory of the closed-loop system to the specified linear switching surface in finite time in spite of the existing uncertainties and unknown transition rates. Finally, an example is given to verify the validity of the theoretical results.

Keywords:

• Markov jump linear systems
• sliding mode control
• partly unknown transition probabilities
• linear matrix inequality (LMI)

Acknowledgements

This work was supported in part by the National 973 Programme of China (Grant No. 2009CB320604), the Funds of National Science of China (Grant Nos. 60974043 and 61273148), the Funds of Doctoral Programme of Ministry of Education, China (Grant No. 20100042110027), the funds for the Author of National Excellent Doctoral Dissertation of People¡¯s Republic of China (Grant No. 201157), the Fundamental Research Funds for the Central Universities (No. N110804001).

Additional information

Notes on contributors

Bo-Chao Zheng

Bo-Chao Zheng was born in 1981, in Shandong, China. He received the Ph.D. degree in College of Information Science and Engineering from Northeastern University, China, in 2012. He is currently a Lecturer at the School of Information and Control, Nanjing University of Information Science & Technology, China. His current research interests include robust control, quantised control, sliding mode control and Markov jump systems.

Guang-Hong Yang

Guang-Hong Yang was born in 1963, in Jilin, China. He received the B.S. and M.S. degrees from Northeast University of Technology, China, in 1983 and 1986, respectively, and the Ph.D. degree in Control Engineering from Northeastern University, China (formerly, Northeast University of Technology), in 1994. He was a Lecturer/Associate Professor with Northeastern University from 1986 to 1995. He joined the Nanyang Technological University in 1996 as a Postdoctoral Fellow. From 2001 to 2005, he was a Research Scientist/Senior Research Scientist with the National University of Singapore. He is currently a Professor at the College of Information Science and Engineering, Northeastern University. His current research interests include fault-tolerant control, fault detection and isolation, non-fragile control systems design and robust control. Dr. Yang is an Associate Editor for the International Journal of Control, Automation, and Systems (IJCAS) and the International Journal of Systems Science (IJSS).