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Reliable finite-time H∞ filtering for discrete time-delay systems with Markovian jump and randomly occurring nonlinearities

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  • Ma, Yuechao
  • Chen, Hui

Abstract

This paper is concerned with the problem of reliable finite-time H∞ filtering for discrete time-varying delay systems with Markovian jump and randomly occurring nonlinearities (RONs). RONs are introduced to model a class of sector-like nonlinearities that occur in a probabilistic way according to a two-dimensional discrete random variables joint distribution. The failures of sensors are quantified by a variable varying in a given interval. The time-varying delay is unknown with given lower and upper bounds. Firstly, the filtering errr dynamic system is constructed based on an H∞ filter, sufficient criteria are provided to guarantee that the resulting filtering error system is stochastic finite-time boundedness and stochastic finite-time H∞ filtering in both normal and fault cases. The gain matrices of the controller and filter are achieved by solving a feasibility problem in terms of linear matrix inequalities with a fixed parameter, respectively. Finally, numerical examples are given to demonstrate the effectiveness of the proposed design approach.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:268:y:2015:i:c:p:897-915
    DOI: 10.1016/j.amc.2015.06.067
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    References listed on IDEAS

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    1. Mao, Xuerong, 1999. "Stability of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 45-67, January.
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    Cited by:

    1. Wang, Guoliang & Cai, Hongyang & Zhang, Qingling & Yang, Chunyu, 2017. "Stabilization of stochastic delay systems via a disordered controller," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 98-109.
    2. 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.
    3. 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.
    4. 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.
    5. Guoliang Wang & Bo Feng, 2016. "Finite-Time Stabilization for Discrete-Time Delayed Markovian Jump Systems with Partially Delayed Actuator Saturation," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-12, November.
    6. 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.
    7. Wang, Guoliang & Li, Zhiqiang & Zhang, Qingling & Yang, Chunyu, 2017. "Robust finite-time stability and stabilization of uncertain Markovian jump systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 377-393.
    8. Yue-Chao Ma & Yang-Fan Liu & Hui Chen, 2017. "Reliable finite-time control of uncertain singular nonlinear Markovian jump systems with bounded transition probabilities and time-varying delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(11), pages 2249-2261, August.
    9. Hyun Kim, Sung, 2019. "Generalized relaxation techniques for robust H∞ filtering of nonhomogeneous Markovian jump systems," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 542-556.
    10. Zhai, Ding & Lu, An-Yang & Dong, Jiuxiang & Zhang, Qing-Ling, 2016. "Asynchronous H∞ filtering for 2D discrete Markovian jump systems with sensor failure," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 60-79.

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