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Robust finite-time H∞ control for discrete-time singular Markovian jump systems with time-varying delay and actuator saturation

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  • Ma, Yuechao
  • Jia, Xiaorui
  • Liu, Deyou

Abstract

In this paper, the problem of robust finite-time H∞ control for discrete-time singular Markovian jump systems with time-varying delay and actuator saturation is studied. First, sufficient conditions that guarantee the systems singular stochastic finite-time boundedness are derived via constructing a delay-dependent Lyapunov–Krasonskii functional and linear matrix inequalities (LMI) approaches. Then the results are extended to singular stochastic finite-time H∞ boundedness. Furthermore, with these conditions and convex optimization arithmetic, the design method of H∞ controller and conditions that ensure the H∞ disturbance attenuation level are obtained. Finally, some numerical examples are presented to illustrate the validity and efficiency of the proposed methods.

Suggested Citation

  • Ma, Yuechao & Jia, Xiaorui & Liu, Deyou, 2016. "Robust finite-time H∞ control for discrete-time singular Markovian jump systems with time-varying delay and actuator saturation," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 213-227.
    • Handle: RePEc:eee:apmaco:v:286:y:2016:i:c:p:213-227
    DOI: 10.1016/j.amc.2016.03.028
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    References listed on IDEAS

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    1. Ma, Yuechao & Fu, Lei & Jing, Yanhui & Zhang, Qingling, 2015. "Finite-time H∞ control for a class of discrete-time switched singular time-delay systems subject to actuator saturation," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 264-283.
    2. E. K. Boukas, 2008. "On State Feedback Stabilization of Singular Systems with Random Abrupt Changes," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 335-345, May.
    3. Ma, Yuechao & Chen, Hui, 2015. "Reliable finite-time H∞ filtering for discrete time-delay systems with Markovian jump and randomly occurring nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 897-915.
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    Cited by:

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    2. Ling Hou & Dongyan Chen & Chan He, 2019. "Finite-Time Nonfragile Dissipative Control for Discrete-Time Neural Networks with Markovian Jumps and Mixed Time-Delays," Complexity, Hindawi, vol. 2019, pages 1-17, June.
    3. Zhou, Yaoyao & Chen, Gang, 2021. "Non-fragile H∞ finite-time sliding mode control for stochastic Markovian jump systems with time delay," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    4. 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).
    5. Zhao, Wenying & Ma, Yuechao & Chen, Aihong & Fu, Lei & Zhang, Yutong, 2019. "Robust sliding mode control for Markovian jump singular systems with randomly changing structure," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 81-96.
    6. Kwon, Nam Kyu & Park, In Seok & Park, PooGyeon, 2017. "H∞ control for singular Markovian jump systems with incomplete knowledge of transition probabilities," Applied Mathematics and Computation, Elsevier, vol. 295(C), pages 126-135.
    7. Wenhai Qi & Yonggui Kao & Xianwen Gao, 2017. "Further results on finite-time stabilisation for stochastic Markovian jump systems with time-varying delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(14), pages 2967-2975, October.
    8. Yan, Zhiguo & Song, Yunxia & Liu, Xiaoping, 2018. "Finite-time stability and stabilization for Itô-type stochastic Markovian jump systems with generally uncertain transition rates," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 512-525.
    9. Nguyen, Khanh Hieu & Kim, Sung Hyun, 2020. "Observer-based control design of semi-Markovian jump systems with uncertain probability intensities and mode-transition-dependent sojourn-time distribution," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    10. Liu, Yangfan & Ma, Yuechao & Wang, Yanning, 2018. "Reliable finite-time sliding-mode control for singular time-delay system with sensor faults and randomly occurring nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 341-357.
    11. Ren, Yong & Li, Kun & Ye, Hui, 2020. "Modeling and anti-swing control for a helicopter slung-load system," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    12. Wei Guan & Lei Fu & Yuechao Ma, 2019. "Finite-Time Filtering for Discrete-Time Singular Markovian Jump Systems with Time Delay and Input Saturation," Complexity, Hindawi, vol. 2019, pages 1-22, April.
    13. Haghighi, Payam & Tavassoli, Babak & Farhadi, Alireza, 2020. "A practical approach to networked control design for robust H∞ performance in the presence of uncertainties in both communication and system," Applied Mathematics and Computation, Elsevier, vol. 381(C).

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