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Relaxed Robust Stabilization Conditions for Nonhomogeneous Markovian Jump Systems with Actuator Saturation and General Switching Policies

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Abstract

This paper investigates the robust control synthesis problem of nonhomogeneous Markovian jump systems with actuator saturation and uncertainties. First of all, to make a comprehensive mode-transition description, three separate mode sets are established according to the property of transition rates. And then, to improve the numerical solvability of inequality conditions dependent on time-varying transition rates, two useful relaxation methods are developed on the basis of the mode sets. Especially, by taking advantage of a new zero-sum constraint, the relaxation process is further evolved such that the conservatism arising from incomplete knowledge of transition rates can be reduced. Lastly, this paper provides the LMI-based conditions capable of estimating the attraction domain as well as of designing a mode-dependent robust control.

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Authors and Affiliations

  1. School of Electrical Engineering, University of Ulsan, Daehak-ro 93, Nam-Gu, Ulsan, 44610, Korea

    Ngoc Hoai An Nguyen & Sung Hyun Kim

Authors
  1. Ngoc Hoai An Nguyen
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  2. Sung Hyun Kim
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Correspondence to Sung Hyun Kim.

Additional information

Recommended by Associate Editors Yang Tang under the direction of Editor Hamid Reza Karimi. This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2018R1D1A1B07041456).

Ngoc Hoai An Nguyen received her B.S. degree in Electrical Engineering from Da Nang University of Technology, Vietnam in 2013. She received her M.S degree in School of Electrical Engineering from University of Ulsan, Ulsan, Korea in 2017. Her research interests are in analysis and synthesis of linear parameter varying systems and fuzzy control systems.

Sung Hyun Kim received his M.S. and Ph.D. degrees in Electrical and Electronic Engineering from POSTECH (Pohang University of Science and Technology), Pohang, Republic of Korea, in 2003 and 2008, respectively. He joined UOU (University of Ulsan), Ulsan, Republic of Korea, in 2011 and is currently a full professor at School of Electrical Engineering in UOU. His research interests cover the field of control design and signal processing for networked/embedded control systems, multi-agent systems, fuzzy-based nonlinear systems, stochastic hybrid systems, and radio frequency identification tag protocol.

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Nguyen, N.H.A., Kim, S.H. Relaxed Robust Stabilization Conditions for Nonhomogeneous Markovian Jump Systems with Actuator Saturation and General Switching Policies. Int. J. Control Autom. Syst. 17, 586–596 (2019). https://doi.org/10.1007/s12555-018-0375-4

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  • DOI: https://doi.org/10.1007/s12555-018-0375-4

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