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A new robust discrete-time sliding mode control design for systems with time-varying delays on state and input and unknown unmatched parameter uncertainties

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  • Ghrab, Sonia
  • Benamor, Anouar
  • Messaoud, Hassani

Abstract

This paper proposes a new robust Discrete-Time Sliding Mode Control (dt-smc) scheme for linear discrete-time delay system. The delays, affecting the state and the input, are assumed to be known, time-varying and bounded. The considered system is also subject to time-varying Unknown But norm-Bounded (ubb) unmatched uncertainties, that act on the state and the delayed state vectors. The designed controller is based on a novel sliding surface. Using a new Lyapunov functional candidate and by introducing slack variables, a less conservative delay-dependent sufficient condition ensuring the asymptotic stability of the closed loop system is derived in terms of Linear Matrix Inequalities (lmis). With respect to that condition a new dt-smc law is synthesized. The proposed control algorithm is applied to an Autonomous Underwater Vehicle (auv). The simulation results demonstrate the effectiveness of the proposed controller.

Suggested Citation

  • Ghrab, Sonia & Benamor, Anouar & Messaoud, Hassani, 2021. "A new robust discrete-time sliding mode control design for systems with time-varying delays on state and input and unknown unmatched parameter uncertainties," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 921-945.
    • Handle: RePEc:eee:matcom:v:190:y:2021:i:c:p:921-945
    DOI: 10.1016/j.matcom.2021.06.009
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    References listed on IDEAS

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    1. Miaadi, Foued & Li, Xiaodi, 2021. "Impulse-dependent settling-time for finite time stabilization of uncertain impulsive static neural networks with leakage delay and distributed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 259-276.
    2. Lin, Xiangze & Zhang, Wanli & Huang, Shuaiting & Zheng, Enlai, 2020. "Finite-time stabilization of input-delay switched systems," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    3. Miaadi, Foued & Li, Xiaodi, 2021. "Impulsive effect on fixed-time control for distributed delay uncertain static neural networks with leakage delay," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    4. Yueqiao Han & Yonggui Kao & Cunchen Gao & Baoping Jiang, 2017. "Robust sliding mode control for uncertain discrete singular systems with time-varying delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(4), pages 818-827, March.
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    Cited by:

    1. Serrano, Fernando E. & Ghosh, Dibakar, 2022. "Robust stabilization and synchronization in a network of chaotic systems with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

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