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H∞ Control of Markovian Jump Systems with Incomplete Knowledge of Transition Probabilities

  • Control Theory and Applications
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Abstract

An H∞ state-feedback controller for Markovian jump systems with incomplete knowledge of transition probabilities and input quantization is proposed. To derive the less conservative stabilization conditions, the conditions are developed into the second-order matrix polynomials of the unknown transition rate using an appropriate weighting method. Furthermore, the proposed controller not only accomplishes an H∞ performance but also removes the matched disturbances and the effect of input quantization. Two examples show the effectiveness of the proposed method.

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Authors and Affiliations

  1. Department of Medical and Mechatronics Engineering, Soonchunhyang University, Asan, Chungnam, Korea

    JaeWook Shin

  2. School of Electronic Engineering, Kumoh National Institute of Technology, Gumi-si, Gyeongsangbuk-do, Korea

    Bum Yong Park

Authors
  1. JaeWook Shin
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  2. Bum Yong Park
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Correspondence to Bum Yong Park.

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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Xiangpeng Xie under the direction of Editor Yoshito Ohta. This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. NRF-2017R1C1B5076575). This work was supported by the Soonchunhyang University Research Fund.

JaeWook Shin received his B.S. degree in electrical engineering and computer science at Kyungpook National University, Korea, in 2008, and his M.S. and Ph.D. degrees in electrical engineering at Pohang University of Science and Technology (POSTECH), Korea, in 2010 and 2014, respectively. Since 2017, he has been affiliated with the Department of Medical and Mechatronics Engineering, Soonchunhyang University, where he is currently a professor. His current research interests include adaptive filter, robust control, and biomedical signal processing.

Bum Yong Park received his M.S. and Ph.D. degrees in Electrical and Electronic Engineering from POSTECH (Pohang University of Science and Technology), Pohang, Korea, in 2011 and 2015, respectively. He joined KIT (Kumoh National Institute of Technology), Gumi, Korea, in 2017 and is currently an assistant professor at School of Electronic Engineering in KIT. His research interests include robust control and signal processing for embedded control systems, robot manipulator system.

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Shin, J., Park, B.Y. H∞ Control of Markovian Jump Systems with Incomplete Knowledge of Transition Probabilities. Int. J. Control Autom. Syst. 17, 2474–2481 (2019). https://doi.org/10.1007/s12555-018-0672-y

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  • DOI: https://doi.org/10.1007/s12555-018-0672-y

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