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Abstract
An extension of a fixed transition probability (TP) Markovian switching model to combine time-varying TPs has offered another set of useful regime-switching models. This paper is concerned with the problem of finite-time H∞ control for a class of discrete-time Markovian jump systems with partly unknown time-varying TPs subject to average dwell time switching. The so-called time-varying TPs mean that the TPs are varying but invariant within an interval. The variation of the TPs considered here is subject to a class of slow switching signal. Based on selecting the appropriate Lyapunov–Krasovskii functional, sufficient conditions of finite-time boundedness of Markovian jump systems are derived and the system trajectory stays within a prescribed bound. Finally, an example is given to illustrate the efficiency of the proposed method.
Acknowledgements
The authors would like to thank the associate editor and the anonymous reviewers for their detailed comments and suggestions. This work was supported by the National Basic Research Program of China (2010CB732501).
Additional information
Notes on contributors
Jun Cheng
Jun Cheng was born in 1987, in Hubei, China. Now he is pursuing a PhD degree in School of Automation Engineering, University of Electronic Science and Technology of China. He has reviewed many journals, for example, ISA Transactions. His current research interests include time-delay systems, neural networks and stability theory.
Hong Zhu
Hong Zhu received the PhD degree from Operational Research and Cybernetics, Sichuan University. He is currently a professor of the School of Automation Engineering at University of Electronic Science and Technology of China. His research works focus on applied mathematics and information science, and more than 50 scholar papers were published in these years.
Shouming Zhong
Shouming Zhong was born on 5 November 1955. He graduated from University of Electronic Science and Technology of China, majoring applied mathematics on differential equation. He is a professor in the School of Mathematical Sciences, University of Electronic Science and Technology of China from June 1997 till date. He is the director of Chinese Mathematical Biology Society, the chair of Biomathematics in Sichuan, and one of the editors of Journal of Biomathematics. He has reviewed many journals, such as Journal of Theory and Application on Control, Journal of Automation, Journal of Electronics, and Journal of Electronics Science. His research interest is stability theorem and its application research of the differential system, the robustness control, neural network and biomathematics.
Yuping Zhang
Yuping Zhang received the PhD degree from School of Automation Engineering, University of Electronic Science and Technology of China. He is currently an associate professor of the School of Automation Engineering at University of Electronic Science and Technology of China. His research interests are in the areas of dynamic behaviours of complex systems.
Yuanyuan Li
Yuanyuan Li received her BS degree from the School of Chinese Language and Literature from University of Hubei University for Nationalities of China in 2011. Now she is pursuing an MA degree in the School of Theory of Literature and Art, Hubei University for Nationalities. Her current research interests include Chinese and western language and culture, comparative poetics and time-delay systems.