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Reliable finite-time control of uncertain singular nonlinear Markovian jump systems with bounded transition probabilities and time-varying delay

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  • Yue-Chao Ma
  • Yang-Fan Liu
  • Hui Chen

Abstract

This paper investigates the problem of reliable finite-time H∞ control for one class of uncertainsingular nonlinear Markovian jump systems with time-varying delay subject to partial information on the transition probabilities. Continuous fault model is more general and practical to serve as the actuator fault. Time delay is a kind of positive time-varying differentiable bounded delays. First, based on a state estimator the resulting closed-loop error system is constructed and sufficient criteria are provided to guarantee that the augmented system is singular stochastic finite-time boundedness and singular stochastic H∞ finite-time boundedness in both normal and fault cases via constructing a delay-dependent Lyapunov–Krasonskii function. Then, the gain matrices of state-feedback controller and state estimator are fixed by solving a feasibility problem in terms of linear matrix inequalities through decoupling technique, respectively. Finally, numerical examples are given to show the validity of the proposed design approach.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:tsysxx:v:48:y:2017:i:11:p:2249-2261
    DOI: 10.1080/00207721.2017.1318972
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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. 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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    1. 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.

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