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Sampled-data Based Dissipativity Control of T-S Fuzzy Markovian Jump Systems under Actuator Saturation with Incomplete Transition Rates

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  • Control Theory and Applications
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Abstract

In this paper, the topic of sampled-data based dissipativity control for Takagi-Sugeno (T-S) fuzzy Markovian jump systems with incomplete transition rates and actuator saturation is addressed. First of all, by constructing an appropriate two-sided closed-loop function that captures the realistic information of sampling pattern, together with the free-matrix-based inequality approach, a sufficient condition is developed to ensure the considered systems to be strictly(\({\cal Q},{\cal S},{\cal R}\))-γ-dissipative. Then, the corresponding mode-dependent sampled-data controllers are designed based on the given dissipativity condition. As a corollary, the controller design is presented for the system without disturbance. Furthermore, an optimization problem is investigated in order to maximize the domain of the attraction. Finally, simulation examples are offered to verify the feasibility of the results.

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Authors and Affiliations

  1. School of Mathematics Science, Liaocheng University, Liaocheng, 252000, P. R. China

    Tianshu Xu, Jianwei Xia & Huasheng Zhang

  2. School of Information Engineering, Henan University of Science and Technology, Luoyang, 471023, China

    Xiaona Song

  3. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China

    Zhen Wang

Authors
  1. Tianshu Xu
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  2. Jianwei Xia
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  3. Xiaona Song
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  4. Zhen Wang
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  5. Huasheng Zhang
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Correspondence to Jianwei Xia.

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Recommended by Associate Editor Yajuan Liu under the direction of Jessie (Ju H.) Park. The authors would like to thank the editors and the reviewers for their comments and constructive suggestions, which helped to greatly improve the paper. This work was supported by the National Natural Science Foundation of China under Grants 61973148, 61773191, 61603170.

Tianshu Xu received her B.Sc. degree in mathematics and applied mathematics from Liaocheng University, Liaocheng, China, in 2018. She is currently a graduate student of School of Mathematical Sciences, Liaocheng University. Her current research interests include Markovian jumping systems, sample-data control, etc.

Jianwei Xia is a professor of the School of Mathematics Science, Liaocheng University. He received a Ph.D. degree in automatic control from Nanjing University of Science and Technology in 2007. From 2010 to 2012, he worked as a Postdoctoral Research Associate in the School of Automation, Southeast University, Nanjing, China. From 2013 to 2014, he worked as a Postdoctoral Research Associate in the Department of Electrical Engineering, Yeungnam University, Kyongsan, Korea. His research topics are robust control,stochastic systems and neural networks.

Xiaona Song received her Ph.D. degree in control science and engineering from Nanjing University of Science and Technology, Nanjing, China, in 2011. From Feb. 2009 to Aug. 2009 and Apr. 2016 to Apr. 2017, she was a visiting scholar with the Department of Electrical Engineering, Utah State University and Southern Illinois University Carbondale, respectively. From June 2019 to Aug. 2019, she was a visiting scholar with the Department of Electrical Engineering, Yeungnam University, Korea. Since 2011, she has been with Henan University of Science and Technology, Luoyang, China, where she is currently a Professor with the School of Information Engineering. Her current research interests include Markov jump distributed parameter systems, complex networks, fractional-order systems and control, fuzzy systems, nonlinear control.

Zhen Wang received his B.S. degree in mathematics from Ocean University of China, Qingdao, China in 2004 and a Ph.D. degree in the School of Automation, Nanjing University of Science and Technology, Nanjing, China in 2014. Since 2004, he has been with Shandong University of Science and Technology, Qingdao, China, where he is currently a Professor and a Doctoral Supervisor. His current research interests include nonlinear control, neural networks, fractional order systems and multi-agent systems.

Huasheng Zhang is an Associate Professor of the School of Mathematics Science, Liaocheng University. He received M.Sc. degree from Shandong Normal University, China, in 2006, and received a Ph.D. degree in automatic control from Shanghai University in 2009. His current research interests include robust control and filtering, time-delay systems, stochastic systems and neural networks.

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Xu, T., Xia, J., Song, X. et al. Sampled-data Based Dissipativity Control of T-S Fuzzy Markovian Jump Systems under Actuator Saturation with Incomplete Transition Rates. Int. J. Control Autom. Syst. 19, 632–645 (2021). https://doi.org/10.1007/s12555-020-0034-4

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