Sampled-data H_∞ filtering for Markovian jump singularly perturbed systems with time-varying delay and missing measurements

ABSTRACT

In this paper, sampled-data H_∞ filtering problem is considered for Markovian jump singularly perturbed systems with time-varying delay and missing measurements. The sampled-data system is represented by a time-delay system, and the missing measurement phenomenon is described by an independent Bernoulli random process. By constructing an ϵ-dependent stochastic Lyapunov–Krasovskii functional, delay-dependent sufficient conditions are derived such that the filter error system satisfies the prescribed H_∞ performance for all possible missing measurements. Then, an H_∞ filter design method is proposed in terms of linear matrix inequalities. Finally, numerical examples are given to illustrate the feasibility and advantages of the obtained results.

KEYWORDS:

• Sampled-data H_∞ filtering
• Markovian jump
• singularly perturbed systems (SPSs)
• missing measurements
• time-varying delay

Acknowledgments

This work was supported by the National Natural Science Foundation of China (61374043, 61603392). The authors would like to thank the editor and anonymous reviewers for their many helpful comments and suggestions improved the quality of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 61374043], [grant number 61603392].

Notes on contributors

Yifang Yan

Yifang Yan received her B.S. degree in Hebei Normal University of Science and Technology, Qinhuangdao, China in 2013. She is currently working toward the Ph.D. degree in China University of Mining and Technology, Xuzhou, China. Her research interests include singularly perturbed systems, sampled-data control.

Chunyu Yang

Chunyu Yangrecieived his B.S. degree in Applied Mathematics and his Ph.D. degree in Control Theory and Control Engineering from Northeastern University, China in 2002 and 2009, respectively. He is currently a full Professor of China University of Mining and Technology, Xuzhou, China. His research interests include singularly perturbed systems and robust control.

Xiaoping Ma

Xiaoping Ma received his B.S., M.S. and Ph.D. degrees from the School of Information and Electrical Engineering of China University of Mining and Technology, Xuzhou, China in 1982, 1989, 2001, respectively. Now he is a Professor of China University of Mining and Technology, Xuzhou, China. His research interests include process control, networked control system and fault detection.

Linna Zhou

Linna Zhou received B.Sc. degree from the Department of Water Conservancy Engineering of North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou, China in 2001. She is now a Professor of China University of Mining and Technology, Xuzhou. And her research interests include singularly perturbed systems, robust control and fuzzy control.