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Stochastic Intermittent Control with Uncertainty

Author

Listed:
  • Zhengqi Ma

    (School of Mathematics and Statistic, Honghe University, Mengzi 661100, China)

  • Hongyin Jiang

    (School of Mathematics and Statistic, Puer University, Puer 665000, China)

  • Chun Li

    (School of Mathematics and Statistic, Honghe University, Mengzi 661100, China)

  • Defei Zhang

    (School of Mathematics and Statistic, Honghe University, Mengzi 661100, China)

  • Xiaoyou Liu

    (School of Mathematics and Computing Sciences, Hunan University of Science and Technology, Xiangtan 411201, China)

Abstract

In this article, we delve into the exponential stability of uncertainty systems characterized by stochastic differential equations driven by G-Brownian motion, where coefficient uncertainty exists. To stabilize the system when it is unstable, we consider incorporating a delayed stochastic term. By employing linear matrix inequalities (LMI) and Lyapunov–Krasovskii functions, we derive a sufficient condition for stabilization. Our findings demonstrate that an unstable system can be stabilized with a control interval within ( θ * , 1 ) . Some numerical examples are provided at the end to validate the correctness of our theoretical results.

Suggested Citation

  • Zhengqi Ma & Hongyin Jiang & Chun Li & Defei Zhang & Xiaoyou Liu, 2024. "Stochastic Intermittent Control with Uncertainty," Mathematics, MDPI, vol. 12(13), pages 1-15, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:1947-:d:1420592
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    References listed on IDEAS

    as
    1. Gao, Fuqing, 2009. "Pathwise properties and homeomorphic flows for stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3356-3382, October.
    2. Peng, Shige, 2008. "Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2223-2253, December.
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