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Finite-time Stability and Stabilization of Markovian Jump Linear Systems Subject to Incomplete Transition Descriptions

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  • Control Theory and Applications
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Abstract

In this paper, the problems of finite-time stability analysis and finite-time stabilization are investigated for Markovian jump linear systems with incomplete transition descriptions. Two sufficient conditions are proposed to guarantee that the system states do not exceed a certain threshold in mean-square sense during a specified time interval for the continuous-time Markovian jump linear systems with partly unknown transition rates and the discrete-time Markovian jump linear systems with partly unknown transition probabilities, respectively. On the basis of the above results, two state feedback controllers are developed to solve the finite-time stochastic stabilization problems of the considered systems in continuous-time domain and discrete-time domain, respectively. For the sake of computational convenience, all the conditions are cast in the format of linear matrix inequalities (LMIs). The main feature of the proposed methods is that the total number of LMIs is much less than that in some existing results. Thus, the solution of the finite-time controllers is more concise both in theory and in engineering. In the end, the validity of the developed theoretical results are demonstrated by two illustrative examples.

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Authors and Affiliations

  1. National University of Defense Technology, Changsha, 410000, P. R. China

    Yuzhu Bai

  2. Sun Yat-sen University, Guangzhou, 510000, P. R. China

    Hui-Jie Sun

  3. Harbin Institute of Technology (Shenzhen), Shenzhen, 518055, P. R. China

    Ai-Guo Wu

Authors
  1. Yuzhu Bai
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  2. Hui-Jie Sun
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  3. Ai-Guo Wu
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Corresponding author

Correspondence to Hui-Jie Sun.

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This work was supported by National Key Research and Development Program of China under Project No.2018AAA0100102, by National Natural Science Foundation of China under Grant Nos.61903103, 61822305, 61690210 and 61690213, by Guangdong Natural Science Foundation under Grant No.2019A1515011576.

Yuzhu Bai received his Ph.D. degree in aerospace engineering from National University of Defense Technology, China, in 2011. He is currently an associate professor at National University of Defense Technology, China. His current research interests include micro-satellite design, spacecraft dynamics and control.

Hui-Jie Sun was born in Inner Mo, P. R. China on August 02, 1988. He received a B.Eng. degree in automation in July 2011 from Harbin Institute of Technology, M.Eng. degree in January 2014 and Ph.D. degree in October 2018 in control science and engineering from Harbin Institute of Technology, Shenzhen. Dr. Sun was a postdoctoral researcher with the School of Electronics and Information Engineering, Harbin Institute of Technology, Shenzhen, from December 2018 to November 2020. He is currently an Assistant Professor in Sun Yat-sen University. His current research interests include stochastic systems, iterative algorithms, neural networks and spacecraft control.

Ai-Guo Wu was born in Gong’an County, Hubei Province, P. R. China on September 20, 1980. He received his B.Eng. degree in automation in July 2002, M.Eng. degree in navigation, guidance and control in July 2004 and Ph.D. degree in control science and engineering in Nov. 2008 all from Harbin Institute of Technology. In Oct. 2008, he joined Harbin Institute of Technology Shenzhen Graduate School as an assistant professor, and in August 2012 he was promoted to a professor. From Jan. 2018, he is a professor in Harbin Institute of Technology, Shenzhen. Dr. Wu was a Research Fellow with the Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong from March 2009 to March 2011. He was a visiting professor with the Department of Electrical, Electronic and Computer Engineering of The University of Western Australia, Australia from July 2013 to July 2014. His research interests include descriptor systems, conjugate product of polynomials, switched system and robust control. He has authored/coauthored one English monograph and more than 80 SCI journal papers. He received the National Natural Science Award (Second Prize) in 2015 from P. R. China, and the National Excellent Doctoral Dissertation Award in 2011 from the Academic Degrees Committee of the State Council and the Ministry of Education of P. R. China. He was supported by the Program for New Century Excellent Talents in University in 2011, and by the National Natural Science Foundation of China for Excellent Young Scholars in 2018. Dr. Wu is a reviewer for American Mathematical Review from 2007. He serves as a Regional Editor of Nonlinear Dynamics and Systems Theory from 2015, and an International Subject Editor of Applied Mathematical Modelling from 2017. He was an Outstanding Reviewer for IEEE Transactions on Automatic Control in 2010.

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Bai, Y., Sun, HJ. & Wu, AG. Finite-time Stability and Stabilization of Markovian Jump Linear Systems Subject to Incomplete Transition Descriptions. Int. J. Control Autom. Syst. 19, 2999–3012 (2021). https://doi.org/10.1007/s12555-020-0505-7

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  • DOI: https://doi.org/10.1007/s12555-020-0505-7

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