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Asynchronous H∞ Control for Positive Discrete-time Markovian Jump Systems

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  • Control Theory and Applications
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Abstract

This paper deals with the asynchronous H∞ control for discrete-time positive Markovian jump systems (PMJSs). In previous results about PMJSs, asynchronous behaviors are always overlooked and the designed controller is based on the synchronization between the system modes and controller modes. Sufficient conditions for stochastic stability are proposed by the use of Lyapunov-Krasovskii functional. The asynchronous controller is designed to ensure the closed-loop system stochastically stable with a prescribed H∞ performance index. All the conditions are given in linear matrix inequality framework. Finally, a pest’s age-structured population dynamic model is illustrated to show the validity of the present design.

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Authors and Affiliations

  1. School of Engineering, Qufu Normal University, Rizhao, 276826, China

    Hui Shang, Wenhai Qi & Guangdeng Zong

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  1. Hui Shang
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  2. Wenhai Qi
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  3. Guangdeng Zong
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Correspondence to Guangdeng Zong.

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Recommended by Associate Editor Mathiyalagan Kalidass under the direction of Editor Yoshito Ohta. This work was supported by National Natural Science Foundation of China under Grant 61703231, Grant 61773235, Grant 61773236, and Grant 61873331, Natural Science Foundation of Shandong under Grant ZR2017QF001, Grant ZR2019YQ29, and Grant ZR2017MF063, Postdoctoral Science Foundation of China under Grant 2017M612235 and Grant 2018T110670, Taishan Scholar Project of Shandong Province under Grant TSQN20161033, Interdisciplinary Scientific Research Projects of Qufu Normal University under Grant xkjjc201905, and Excellent Experiment Project of Qufu Normal University under Grant jp201728.

Hui Shang was born in Dezhou, Shandong Province, China, in 1993. She received her B.S. degree in Ludong university in 2016. Currently, she is studying for a Ph.D. in Qufu Normal University, Rizhao, China. Her research interests are switched systems, positive systems, eventtriggered control, etc.

Wenhai Qi was born in Taian, Shandong Province, P. R. China, in 1986. He received his B.S. degree in automation from Qufu Normal University in 2008 and his M.S. degree from Qufu Normal University in 2013. In 2016, he received his Ph.D. degree in control theory and control engineering from Northeastern University. He works in Qufu Normal University. His research work focus on Markovian jump systems, positive systems, etc.

Guangdeng Zong was born in Linyi, China, in 1976. He received his B.S. and M.S. degrees in mathematics from Qufu Normal University, Qufu, China, in 1999 and 2002, respectively, and his Ph.D. degree in the control science and engineering from the School of Automation, Southeast University, Nanjing, China, in 2005. He was a Postdoctor with the School of Automation, Nanjing University of Science and Technology, Nanjing, from 2006 to 2009. In 2010, he was a Visiting Professor with the Department of Electrical and Computer Engineering, Utah State University, Logan, UT, USA. In 2012, he was a Visiting Fellow with the School of Computing, Engineering and Mathematics, University of Western Sydney, Penrith, NSW, Australia. In 2016, he was a Visiting Professor with the Institute of Information Science, Academia Sinica, Taipei, Taiwan. Since 2010, he has been a Full Professor with Qufu Normal University. His research has been widely published in international journals and conferences. His current research interests include hybrid systems, Markovian jump systems, time-delay systems, \(\mathcal{H}_\infty\) control, and filtering and their applications.

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Shang, H., Qi, W. & Zong, G. Asynchronous H∞ Control for Positive Discrete-time Markovian Jump Systems. Int. J. Control Autom. Syst. 18, 431–438 (2020). https://doi.org/10.1007/s12555-018-0107-9

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  • DOI: https://doi.org/10.1007/s12555-018-0107-9

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