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Robust observer and observer-based control designs for discrete one-sided Lipschitz systems subject to uncertainties and disturbances

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  • Nguyen, Cuong M.
  • Pathirana, Pubudu N.
  • Trinh, Hieu

Abstract

In this paper, we study the robust observer design and observer-based control design problems for a class of discrete one-sided Lipschitz systems subject to uncertainties and disturbances. The nonlinearities are assumed to be one-sided Lipschitz and quadratically inner-bounded. By utilizing a new approach which is an extension of the H∞ filtering method, our robust observer design can relax some limitations in existing works. In order to derive design conditions in terms of linear matrix inequalities, several mathematical techniques are appropriately used to linearize the bilinear terms which unavoidably emerge in observer and observer-based control designs for discrete-time uncertain systems. Via a numerical example, we show that while existing works fail, our results work effectively.

Suggested Citation

  • Nguyen, Cuong M. & Pathirana, Pubudu N. & Trinh, Hieu, 2019. "Robust observer and observer-based control designs for discrete one-sided Lipschitz systems subject to uncertainties and disturbances," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 42-53.
    • Handle: RePEc:eee:apmaco:v:353:y:2019:i:c:p:42-53
    DOI: 10.1016/j.amc.2019.01.064
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    References listed on IDEAS

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    1. Wang, Jing & Liang, Kun & Huang, Xia & Wang, Zhen & Shen, Hao, 2018. "Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 247-262.
    2. Jiao, Shiyu & Shen, Hao & Wei, Yunliang & Huang, Xia & Wang, Zhen, 2018. "Further results on dissipativity and stability analysis of Markov jump generalized neural networks with time-varying interval delays," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 338-350.
    3. M. C. Nguyen & H. Trinh & P. T. Nam, 2016. "Linear functional observers with guaranteed ε-convergence for discrete time-delay systems with input/output disturbances," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(13), pages 3193-3205, October.
    4. Nguyen, Minh Cuong & Trinh, Hieu, 2016. "Unknown input observer design for one-sided Lipschitz discrete-time systems subject to time-delay," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 57-71.
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    Cited by:

    1. Jiang, Ling & Cao, Jinde & Xiong, Lianglin, 2019. "Generalized multiobjective robustness and relations to set-valued optimization," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 599-608.
    2. Hussain, Muntazir & Rehan, Muhammad & Ahmed, Shakeel & Abbas, Tanveer & Tufail, Muhammad, 2020. "A novel approach for static anti-windup compensation of one-sided Lipschitz systems under input saturation," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    3. Zhang, Tu & Li, Liwei & Shen, Mouquan, 2021. "Interval observer-based finite-time control for linear parameter-varying systems," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    4. Nguyen, Cuong M. & Tan, Chee Pin & Trinh, Hieu, 2021. "State and delay reconstruction for nonlinear systems with input delays," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    5. Bicheng Guo & Jiang Guo, 2019. "Feedback Linearization and Reaching Law Based Sliding Mode Control Design for Nonlinear Hydraulic Turbine Governing System," Energies, MDPI, vol. 12(12), pages 1-19, June.

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