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Robust control of uncertain semi-Markovian jump systems using sliding mode control method

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  • Zhou, Qi
  • Yao, Deyin
  • Wang, Jiahui
  • Wu, Chengwei

Abstract

The problem of robust adaptive sliding mode control for semi-Markovian jump systems with actuator faults is investigated in this paper. The uncertainties considered in this paper satisfy norm-bounded form, and bounds of nonlinearity, actuator faults and external disturbance are unknown. Then, the influences of the actuator faults, unknown nonlinearity and disturbance can be effectively attenuated via a novel adaptive sliding mode controller. The reachability of sliding mode surface can be guaranteed by the adaptive sliding mode controller. Using Lyapunov stability theory, sufficient conditions are derived to guarantee the stochastic stability of the sliding mode dynamics. Finally, a numerical example is exploited to demonstrate the effectiveness of the proposed method.

Suggested Citation

  • Zhou, Qi & Yao, Deyin & Wang, Jiahui & Wu, Chengwei, 2016. "Robust control of uncertain semi-Markovian jump systems using sliding mode control method," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 72-87.
    • Handle: RePEc:eee:apmaco:v:286:y:2016:i:c:p:72-87
    DOI: 10.1016/j.amc.2016.03.013
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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.
    2. Mao, Xuerong, 1999. "Stability of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 45-67, January.
    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. Pradeep, C. & Cao, Yang & Murugesu, R. & Rakkiyappan, R., 2019. "An event-triggered synchronization of semi-Markov jump neural networks with time-varying delays based on generalized free-weighting-matrix approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 41-56.
    3. Nguyen, Ngoc Hoai An & Kim, Sung Hyun, 2021. "Asynchronous dissipative control design for semi-Markovian jump systems with uncertain probability distribution functions of sojourn-time," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    4. Ran, Suzhen & Xue, Yanmei & Zheng, Bo-Chao & Wang, Zhenyou, 2017. "Quantized feedback fuzzy sliding mode control design via memory-based strategy," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 283-295.
    5. Liang, Hongjing & Zhou, Yu & Ma, Hui & Wu, Qinghui & Yu, Zhandong, 2018. "Distributed-observer-based output synchronization for heterogeneous double-integral networks," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 535-544.
    6. Kaviarasan, Boomipalagan & Kwon, Oh-Min & Park, Myeong Jin & Sakthivel, Rathinasamy, 2023. "Reduced-order filtering for semi-Markovian jump systems against randomly occurring false data injection attacks," Applied Mathematics and Computation, Elsevier, vol. 444(C).
    7. Hongqian Lu & Chaoqun Guo & Yue Hu & Wuneng Zhou, 2019. "Event-Triggered Stability Analysis of Semi-Markovian Jump Networked Control System with Actuator Faults and Time-Varying Delay via Bessel–Legendre Inequalities," Complexity, Hindawi, vol. 2019, pages 1-16, October.
    8. 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.
    9. Kong, Chuifeng & Ma, Yuechao & Liu, Deyou, 2019. "Observer-based quantized sliding mode dissipative control for singular semi-Markovian jump systems," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.

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