非均匀传输线方程的稳定性和谱分析

数学物理学报 ›› 2026, Vol. 46 ›› Issue (1): 259-269.

非均匀传输线方程的稳定性和谱分析

张乐(), 赵东霞^*(), 王婧雯(), 张姣姣()

中北大学数学学院太原 030051

收稿日期:2025-04-27 修回日期:2025-09-30 出版日期:2026-02-26 发布日期:2026-01-19
通讯作者: 赵东霞 E-mail:2399915366@qq.com;zhaodongxia6@sina.com;1500068705@qq.com;2638809327@qq.com
作者简介:张乐, Email: 2399915366@qq.com;
王婧雯, Email: 1500068705@qq.com;
张姣姣, Email: 2638809327@qq.com
基金资助:
山西省自然科学基金面上项目(202403021221124);山西省研究生教育创新计划(2025XX19)

Stability and Spectral Analysis of Nonuniform Transmission Line Equations

Le Zhang(), Dongxia Zhao^*(), Jingwen Wang(), Jiaojiao Zhang()

School of Mathematics, North University of China, Taiyuan 030051

Received:2025-04-27 Revised:2025-09-30 Online:2026-02-26 Published:2026-01-19
Contact: Dongxia Zhao E-mail:2399915366@qq.com;zhaodongxia6@sina.com;1500068705@qq.com;2638809327@qq.com
Supported by:
Natural Science Fundamental General Project of Shanxi Province(202403021221124);Graduate Education Innovation Program Project of Shanxi Province(2025XX19)

摘要/Abstract

摘要：

该文对非均匀传输线方程进行黎曼坐标变换和坐标缩放, 建立了一类具有变系数的双曲 PDE-PDE 耦合系统. 假设边界条件的控制输入电压恒为常量, 得到了系统的比例反馈边界条件. 然后将闭环系统改写为抽象发展方程的形式, 利用半群方法和等价范数定理得出反馈控制参数的耗散性条件, 保证系统算子的耗散性. 最后, 对系统算子进行谱分析, 利用矩阵束方法推导出了特征值的渐近表达式.

关键词: 非均匀传输线, Lyapunov 函数, 变系数双曲型系统, 矩阵束方法

Abstract:

This article applies Riemann coordinate transformation and coordinate scaling to non-uniform transmission line equations, and establishes a class of hyperbolic PDE-PDE coupled systems with variable coefficients. Assuming that the control input voltage of the boundary condition remains constant, the proportional feedback boundary condition of the system is obtained. Then rewrite the closed-loop system into the form of abstract evolution equations, and use the semigroup method and equivalent norm theorem to obtain the dissipativity conditions of feedback control parameters, ensuring the dissipativity of system operators. Finally, spectral analysis was conducted on the system operators, and the asymptotic expression of the eigenvalues was derived using the matrix operator pencil method.

Key words: nonuniform transmission line, Lyapunov function, hyperbolic system with variable coefficients, matrix operator pencil method

中图分类号:

O231.4

张乐, 赵东霞, 王婧雯, 张姣姣. 非均匀传输线方程的稳定性和谱分析[J]. 数学物理学报, 2026, 46(1): 259-269.

Le Zhang, Dongxia Zhao, Jingwen Wang, Jiaojiao Zhang. Stability and Spectral Analysis of Nonuniform Transmission Line Equations[J]. Acta mathematica scientia,Series A, 2026, 46(1): 259-269.

图/表 1

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