联合抗阻尼耦合波动方程的延迟位移反馈镇定

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2025-04-23 DOI:10.1016/j.jmaa.2025.129616

Yi-Ning Wang, Jun-Min Wang

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引用次数: 0

摘要

本文研究了具有联合抗阻尼的两个耦合波动方程的镇定问题。通过设计一种新颖的变换，将波动系统转化为在结合点处具有阻尼项的系统，并设计了具有延迟位移的反馈控制器。通过数学归纳法证明了变换的可逆性。利用Riesz基方法和PDE方法，建立了非耗散闭环系统的适定性和指数稳定性。仿真结果验证了反馈控制律的有效性。

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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Delayed displacement feedback stabilization of two coupled wave equations with joint anti-damping

In this paper, we consider the stabilization problem of two coupled wave equations with joint anti-damping. By designing a novel transformation, the wave system is transformed into a system with damping term at the joint point, and the feedback controller with delayed displacement is designed. The invertibility of the transformation is proven through the mathematical induction. Furthermore, by using the Riesz basis method and the PDE approach, the well-posedness and exponential stability of the non-dissipative closed-loop system are established. Simulation results are presented to verify the effectiveness of the feedback control law.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.