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Novel Robust Estimation-Based Control of One-Sided Lipschitz Nonlinear Systems Subject to Output and Input Delays

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  • Sohaira Ahmad

    (Department of Electrical Engineering, Wah Engineering College, University of Wah, Wah Cantt 47040, Pakistan
    These authors have contributed equally to this work and first authorship.)

  • Muhammad Rehan

    (Department of Electrical Engineering, Pakistan Institute of Engineering and Applied Sciences (PIEAS), Islamabad 44000, Pakistan)

  • Anas Ibrar

    (Department of Electrical Engineering, Wah Engineering College, University of Wah, Wah Cantt 47040, Pakistan)

  • Muhammad Umair Ali

    (Department of Artificial Intelligence and Robotics, Sejong University, Seoul 05006, Republic of Korea
    These authors have contributed equally to this work and first authorship.)

  • Amad Zafar

    (Department of Artificial Intelligence and Robotics, Sejong University, Seoul 05006, Republic of Korea)

  • Seong Han Kim

    (Department of Artificial Intelligence and Robotics, Sejong University, Seoul 05006, Republic of Korea)

Abstract

This paper highlights the design of a controller established on estimated states for one-sided Lipschitz (OSL) nonlinear systems subject to output and input delays. The controller has been devised by involving Luenberger-like estimated states. The stability of the time-delayed nonlinear system is reckoned by assuming a Lyapunov functional for delayed dynamics and for which a delay-range dependent criterion is posed with a delay ranging between known upper and lower bounds. The time derivative of the functional is further exploited with linear matrix inequality (LMI) procedures, and employing Wirtinger’s inequality for the integral terms instead of the traditional and more conservative Jensen’s condition. Moreover, a sufficient and necessary solution is derived for the proposed design by involving the tedious decoupling technique to attain controller and observer gain simultaneously. The proposed methodology validates the observer error stability between observers and states asymptotically. The solution of matrix inequalities was obtained by employing cone-complementary linearization techniques to solve the tiresome constraints through simulation tools by convex optimization. Additionally, a novel scheme of an observer-based controller for the linear counterpart is also derived for one-sided Lipschitz nonlinear systems with multiple delays. Finally, the effectualness of the presented observer-based controller under input and output delays for one-sided Lipschitz nonlinear systems is validated by considering a numerical simulation of mobile systems in Cartesian coordinates.

Suggested Citation

  • Sohaira Ahmad & Muhammad Rehan & Anas Ibrar & Muhammad Umair Ali & Amad Zafar & Seong Han Kim, 2024. "Novel Robust Estimation-Based Control of One-Sided Lipschitz Nonlinear Systems Subject to Output and Input Delays," Mathematics, MDPI, vol. 12(9), pages 1-35, April.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:9:p:1374-:d:1386864
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    References listed on IDEAS

    as
    1. Du, Xiao-Kun & Zhao, Hui & Chang, Xiao-Heng, 2015. "Unknown input observer design for fuzzy systems with uncertainties," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 108-118.
    2. Chen, Guoliang & Xia, Jianwei & Zhuang, Guangming & Zhao, Junsheng, 2018. "Improved delay-dependent stabilization for a class of networked control systems with nonlinear perturbations and two delay components," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 1-17.
    3. Majeed, Raafia & Ahmad, Sohaira & Rehan, Muhammad, 2015. "Delay-range-dependent observer-based control of nonlinear systems under input and output time-delays," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 145-159.
    4. Xiao-Heng Chang & Guang-Hong Yang & Haibo Wang, 2011. "Observer-based -control for discrete-time T–S fuzzy systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(10), pages 1801-1809.
    5. Sohaira Ahmad & Raafia Majeed & Keum-Shik Hong & Muhammad Rehan, 2015. "Observer Design for One-Sided Lipschitz Nonlinear Systems Subject to Measurement Delays," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-13, March.
    6. Shaheen, Bilal & Nazir, Muhammad Shahid & Rehan, Muhammad & Ahmad, Sohaira, 2020. "Robust generalized observer design for uncertain one-sided Lipschitz systems," Applied Mathematics and Computation, Elsevier, vol. 365(C).
    Full references (including those not matched with items on IDEAS)

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