半线性分布式系统中分数输出的最优反馈稳定

Q1 Mathematics

Partial Differential Equations in Applied Mathematics Pub Date : 2024-09-18 DOI:10.1016/j.padiff.2024.100911

Marouane Karim , Issam Khaloufi , Imane Dehaj , Rachik Mostafa

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引用次数: 0

摘要

本研究探讨了半线性分布式系统中状态空间分数导数的稳定问题，使用的是阶数为 α 的黎曼-刘维尔导数，其中 α 位于 0,1 的区间内。主要目标是开发有效的反馈控制策略，确保分数输出的强稳定和弱稳定。此外，我们还解决了分数最小化问题，以提高系统性能。我们提供了一个数值模拟示例，以证明所提出的稳定定理的实际意义。

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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Optimal feedback stabilization of fractional output in semilinear distributed systems

This study explores the stabilization of state–space fractional derivatives in semilinear distributed systems, using the Riemann–Liouville derivative of order $α$ , where $α$ lies within the interval $(0, 1)$ . The main objective is to develop effective feedback control strategies that ensure both strong and weak stabilization of fractional outputs. Additionally, we tackle a fractional minimization problem to enhance the system’s performance. A numerical simulation example is provided to demonstrate the practical significance of the proposed stabilization theorems.

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