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Mittag–Leffler stabilization for short memory fractional reaction-diffusion systems via intermittent boundary control

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  • Li, Xing-Yu
  • Wu, Kai-Ning
  • Liu, Xiao-Zhen

Abstract

Under the designed intermittent boundary controller, the Mittag–Leffler stabilization for short memory fractional reaction-diffusion systems (SMFRDSs) is investigated. By employing the Lyapunov functional method and kinds of inequalities, we derive a sufficient criterion that ensures the Mittag–Leffler stability for SMFRDSs. Robust Mittag–Leffler stability is also considered when there are uncertainties in SMFRDSs. Besides, we analyze how the control gains and diffusion coefficient matrix affect the stability. Finally, we carry out the numerical simulation based on the above results.

Suggested Citation

  • Li, Xing-Yu & Wu, Kai-Ning & Liu, Xiao-Zhen, 2023. "Mittag–Leffler stabilization for short memory fractional reaction-diffusion systems via intermittent boundary control," Applied Mathematics and Computation, Elsevier, vol. 449(C).
    • Handle: RePEc:eee:apmaco:v:449:y:2023:i:c:s0096300323001285
    DOI: 10.1016/j.amc.2023.127959
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    References listed on IDEAS

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    1. Chang, Wenting & Zhu, Song & Li, Jinyu & Sun, Kaili, 2018. "Global Mittag–Leffler stabilization of fractional-order complex-valued memristive neural networks," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 346-362.
    2. Han, Xin-Xin & Wu, Kai-Ning & Ding, Xiaohua, 2020. "Finite-time stabilization for stochastic reaction-diffusion systems with Markovian switching via boundary control," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    3. 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).
    4. Chen, Wei-Ching, 2008. "Nonlinear dynamics and chaos in a fractional-order financial system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1305-1314.
    5. Yang, Xujun & Li, Chuandong & Huang, Tingwen & Song, Qiankun, 2017. "Mittag–Leffler stability analysis of nonlinear fractional-order systems with impulses," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 416-422.
    6. Hou, Mimi & Xi, Xuan-Xuan & Zhou, Xian-Feng, 2021. "Boundary control of a fractional reaction-diffusion equation coupled with fractional ordinary differential equations with delay," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    7. Zhou, Ya & Wan, Xiaoxiao & Huang, Chuangxia & Yang, Xinsong, 2020. "Finite-time stochastic synchronization of dynamic networks with nonlinear coupling strength via quantized intermittent control," Applied Mathematics and Computation, Elsevier, vol. 376(C).
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    Cited by:

    1. Jia, Wenwen & Xie, Jingu & Guo, Haihua & Wu, Yongbao, 2024. "Intermittent boundary control for fixed-time stability of reaction–diffusion systems," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    2. Huang, Zhuoyuan & Bao, Haibo, 2024. "Output synchronization of reaction-diffusion neural networks with multiple output couplings via generalized intermittent control," Applied Mathematics and Computation, Elsevier, vol. 477(C).

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