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Robust finite-time stability and stabilization of uncertain Markovian jump systems with time-varying delay

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Listed:
  • Wang, Guoliang
  • Li, Zhiqiang
  • Zhang, Qingling
  • Yang, Chunyu

Abstract

This paper deals with the robust finite-time stability and stabilization problems of uncertain stochastic delayed jump systems, where the uncertainty is in the form of additive perturbations and exists in the drift and diffusion sections simultaneously. Though perturbation, time-varying delay and Brownian motion existing at the same time, two conditions checking its robust finite-time stability are proposed by a mode-dependent parameter approach, which are different from some existing methods. Based on the proposed results, sufficient conditions for the existence of the state-feedback controller are provided with LMIs, which could be solved directly. It is seen that all the features of the underlying system such as time-varying delay, perturbation, diffusion, mode-dependent parameters and uncertain transition rate matrix play important roles in the system analysis and synthesis of finite-time stability. Finally, numerical examples are used to demonstrate the effectiveness and superiority of the proposed methods.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:293:y:2017:i:c:p:377-393
    DOI: 10.1016/j.amc.2016.08.044
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    References listed on IDEAS

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    1. Wang, Guoliang, 2016. "Mode-independent control of singular Markovian jump systems: A stochastic optimization viewpoint," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 155-170.
    2. Jianwei Xia & Changyin Sun & Xiang Teng & Hongbin Zhang, 2014. "Delay-segment-dependent robust stability for uncertain discrete stochastic Markovian jumping systems with interval time delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(3), pages 271-282.
    3. 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.
    4. Qi, Wenhai & Gao, Xianwen, 2016. "H∞ observer design for stochastic time-delayed systems with Markovian switching under partly known transition rates and actuator saturation," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 80-97.
    5. 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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