Exponential stabilization for spatial multiple-fractional advection-diffusion-reaction system

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation Pub Date : 2025-03-21 DOI:10.1016/j.amc.2025.129409

Xing-Yu Li , Kai-Ning Wu , Zhan-Wen Yang

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引用次数: 0

Abstract

The exponential stabilization for spatial multiple-fractional advection-diffusion-reaction system (SMFADRS) is considered, and for the disturbed SMFADRS, the finite-time

H_{\infty}

stabilization is investigated. To ensure the considered system to achieve the desired performance, a distributed controller is designed to be located in the sub-intervals of the whole spatial domain. Then, by deriving an improved fractional Poincare's inequality and resorting to the Lyapunov functional method, the sufficient criteria of exponential stability and finite-time

H_{\infty}

performance are obtained. Besides, we also explore the effect of the space domain and its division, the control gain, the distribution of controller and the fractional order on the stability. Moreover, we apply the obtained theoretical results to address the control problem of the groundwater pollution, and the corresponding numerical simulations are performed to show the effectiveness of our results.

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空间多分式平流-扩散-反应系统的指数稳定性

研究了空间多分数阶平流扩散反应系统（SMFADRS）的指数镇定问题，并对受扰动的SMFADRS进行了有限时间H∞镇定问题的研究。为了保证所考虑的系统达到预期的性能，在整个空间域的子区间上设计了分布式控制器。然后，通过推导改进的分数阶Poincare不等式，利用Lyapunov泛函方法，得到了指数稳定性和有限时间H∞性能的充分判据。此外，我们还探讨了空间域及其划分、控制增益、控制器的分布和分数阶对稳定性的影响。将所得理论结果应用于地下水污染控制问题，并进行了相应的数值模拟，验证了所得理论结果的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematics and Computation 数学-应用数学

CiteScore

7.90

自引率

10.00%

发文量

755

审稿时长

36 days

期刊介绍： Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results. In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.