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Discrete-time control for highly nonlinear neutral stochastic delay systems

Author

Listed:
  • Song, Gongfei
  • Zhang, Zimeng
  • Zhu, Yanan
  • Li, Tao

Abstract

This work explores the discrete-time state feedback control problem for neutral stochastic delay systems(NSDSs) in which coefficients satisfy highly nonlinear. Due to the highly nonlinear, the neutral term and discrete time observation value, many conventional methods are not applicable. A more general Lyapunov function is constructed to prove that the designed controller can stabilize the corresponding systems. In addition, H∞-stable, asymptotically stable and exponentially stable of the corresponding studied systems are presented. Then, a numerical case is demonstrated to verify the correctness and validity of the proposed theoretical results.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:430:y:2022:i:c:s0096300322003873
    DOI: 10.1016/j.amc.2022.127313
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    References listed on IDEAS

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    1. Qiu, Qinwei & Liu, Wei & Hu, Liangjian & Mao, Xuerong & You, Surong, 2016. "Stabilization of stochastic differential equations with Markovian switching by feedback control based on discrete-time state observation with a time delay," Statistics & Probability Letters, Elsevier, vol. 115(C), pages 16-26.
    2. Zhuang, Guangming & Xu, Shengyuan & Xia, Jianwei & Ma, Qian & Zhang, Zhengqiang, 2019. "Non-fragile delay feedback control for neutral stochastic Markovian jump systems with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 21-32.
    3. Feng, Lichao & Liu, Lei & Wu, Zhihui & Liu, Qiumei, 2021. "Stability analysis for nonlinear Markov jump neutral stochastic functional differential systems," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    4. Mao, Xuerong & Shen, Yi & Yuan, Chenggui, 2008. "Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 118(8), pages 1385-1406, August.
    5. Mao, Xuerong, 1999. "Stability of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 45-67, January.
    6. 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.
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