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Robust sliding mode control for uncertain discrete singular systems with time-varying delays

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  • Yueqiao Han
  • Yonggui Kao
  • Cunchen Gao
  • Baoping Jiang

Abstract

This paper investigates robust sliding mode control (SMC) for discrete singular systems which include time-varying delays, parameter uncertainties and nonlinear perturbations. An appropriate discrete sliding surface function is constructed such that the corresponding sliding mode dynamics are gained. By using some free-weighting matrices, a linear matrix inequality constraint is established to make sure that the closed-loop system is regular, causal and stable. Furthermore, in consideration of the improved discrete reaching condition, an SMC law is synthesised for reaching motion and the chattering can be weakened, while few existing papers focus on how to employ it to study the SMC problem for the discrete singular systems with time-varying delays. At last, the designed law is tested through an example.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:tsysxx:v:48:y:2017:i:4:p:818-827
    DOI: 10.1080/00207721.2016.1216200
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    References listed on IDEAS

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    1. Jiang, Baoping & Gao, Cunchen & Xie, Jing, 2015. "Passivity based sliding mode control of uncertain singular Markovian jump systems with time-varying delay and nonlinear perturbations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 187-200.
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    Cited by:

    1. Lu, Xuchen & Ren, Junchao, 2023. "Robust (Q,S,R)−α-dissipative event-triggered sliding mode control of discrete T-S fuzzy descriptor systems with partial unmeasurable premise variables," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    2. Obaid Alshammari & Mourad Kchaou & Houssem Jerbi & Sondess Ben Aoun & Víctor Leiva, 2022. "A Fuzzy Design for a Sliding Mode Observer-Based Control Scheme of Takagi-Sugeno Markov Jump Systems under Imperfect Premise Matching with Bio-Economic and Industrial Applications," Mathematics, MDPI, vol. 10(18), pages 1-28, September.
    3. 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.
    4. Qi, Wenhai & Kao, Yonggui & Gao, Xianwen & Wei, Yunliang, 2018. "Controller design for time-delay system with stochastic disturbance and actuator saturation via a new criterion," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 535-546.
    5. Hu, Jun & Zhang, Panpan & Kao, Yonggui & Liu, Hongjian & Chen, Dongyan, 2019. "Sliding mode control for Markovian jump repeated scalar nonlinear systems with packet dropouts: The uncertain occurrence probabilities case," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    6. Su, Qingyu & Wang, Handong & Sun, Chaowei & Li, Bo & Li, Jian, 2022. "Cyber-attacks against cyber-physical power systems security: State estimation, attacks reconstruction and defense strategy," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    7. Chu, Xiaoan & Li, Muguo, 2019. "Observer-based model following sliding mode tracking control of discrete-time linear networked systems with two-channel event-triggered schemes and quantizations," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 428-448.
    8. Mu, Yunfei & Zhang, Huaguang & Su, Hanguang & Wang, Yingchun, 2021. "Robust normalization and H∞ stabilization for uncertain Takagi-Sugeno fuzzy singular systems with time-delays," Applied Mathematics and Computation, Elsevier, vol. 388(C).
    9. Liu, Guobao & Xu, Shengyuan & Wei, Yunliang & Qi, Zhidong & Zhang, Zhengqiang, 2018. "New insight into reachable set estimation for uncertain singular time-delay systems," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 769-780.

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