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Robust discrete-state-feedback stabilization of hybrid stochastic systems with time-varying delay based on Razumikhin technique

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  • Li, Yuyuan
  • Lu, Jianqiu
  • Kou, Chunhai
  • Mao, Xuerong
  • Pan, Jiafeng

Abstract

This paper deals with the robust stabilization of continuous-time hybrid stochastic systems with time-varying delay by feedback controls based on discrete-time state observations. By employing the Razumikhin technique, delay-independent criteria to determine controllers and time lags are established just under a weaker condition that the time-varying delay should be a bounded function. Meanwhile, for the nondelay system, we obtain a better bound on the duration τ between two consecutive state observations. The new theory developed in this paper improves the existing results. Numerical examples are provided to demonstrate the effectiveness of our results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:139:y:2018:i:c:p:152-161
    DOI: 10.1016/j.spl.2018.02.058
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    References listed on IDEAS

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    1. 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.
    2. Li, Bing, 2017. "A note on stability of hybrid stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 299(C), pages 45-57.
    3. 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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    1. Shen Wang & Guohe Huang & Yurui Fan, 2018. "A Multistage Distribution-Generation Planning Model for Clean Power Generation under Multiple Uncertainties—A Case Study of Urumqi, China," Sustainability, MDPI, vol. 10(9), pages 1-30, September.

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