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Robustly exponential stabilization of hybrid uncertain systems by feedback controls based on discrete-time observations

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  • You, Surong
  • Hu, Liangjian
  • Mao, Wei
  • Mao, Xuerong

Abstract

This paper deals with the problem of stabilizing a hybrid stochastic system with norm bounded uncertainties. State-feedback controls based on discrete-time observations are designed in the drift and diffusion parts of the system. The controlled system will be robustly exponentially stable in mean-square. Applying linear matrix inequality techniques, criteria to determine controllers and time lags are developed. One numerical example is given to verify our techniques.

Suggested Citation

  • You, Surong & Hu, Liangjian & Mao, Wei & Mao, Xuerong, 2015. "Robustly exponential stabilization of hybrid uncertain systems by feedback controls based on discrete-time observations," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 8-16.
    • Handle: RePEc:eee:stapro:v:102:y:2015:i:c:p:8-16
    DOI: 10.1016/j.spl.2015.03.006
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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.
    2. He, Yong & Wang, Qing-Guo & Zheng, Wei-Xing, 2005. "Global robust stability for delayed neural networks with polytopic type uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1349-1354.
    3. Udom, Akaninyene Udo, 2012. "Exponential stabilization of stochastic interval system with time dependent parameters," European Journal of Operational Research, Elsevier, vol. 222(3), pages 523-528.
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    Citations

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    Cited by:

    1. Li, Jin & Guo, Ying & Liu, Xiaotong & Zhang, Yifan, 2024. "Stabilization of highly nonlinear stochastic coupled systems with Markovian switching under discrete-time state observations control," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    2. Luo, Tianjiao, 2019. "Stabilization of multi-group models with multiple dispersal and stochastic perturbation via feedback control based on discrete-time state observations," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 396-410.
    3. Yu, Peilin & Deng, Feiqi, 2022. "Stabilization analysis of Markovian asynchronous switched systems with input delay and Lévy noise," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    4. Zhang, Tian & Chen, Huabin, 2019. "The stability with a general decay of stochastic delay differential equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 294-307.
    5. Wu, Yongbao & Guo, Haihua & Li, Wenxue, 2020. "Finite-time stabilization of stochastic coupled systems on networks with Markovian switching via feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    6. Fan, Lina & Lv, Yuan & Zhu, Quanxin, 2023. "Stability analysis of discrete-time switched stochastic non-autonomous systems with external inputs and time-varying delays under partially unstable subsystems," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    7. Song, Minghui & Geng, Yidan & Liu, Mingzhu, 2021. "Stability equivalence among stochastic differential equations and stochastic differential equations with piecewise continuous arguments and corresponding Euler-Maruyama methods," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    8. Mukama, Denis Sospeter & Ghani, Mohammad & Mbalawata, Isambi Sailon, 2023. "Persistence, Extinction, and boundedness in pth moment of hybrid stochastic logistic systems by delay feedback control based on discrete-time observation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 661-677.
    9. Song, Gongfei & Zhang, Zimeng & Zhu, Yanan & Li, Tao, 2022. "Discrete-time control for highly nonlinear neutral stochastic delay systems," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    10. Li, Yuyuan & Lu, Jianqiu & Kou, Chunhai & Mao, Xuerong & Pan, Jiafeng, 2018. "Robust discrete-state-feedback stabilization of hybrid stochastic systems with time-varying delay based on Razumikhin technique," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 152-161.
    11. Feng, Lichao & Liu, Qiumei & Cao, Jinde & Zhang, Chunyan & Alsaadi, Fawaz, 2022. "Stabilization in general decay rate of discrete feedback control for non-autonomous Markov jump stochastic systems," Applied Mathematics and Computation, Elsevier, vol. 417(C).

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