非均匀传输线方程的稳定性和谱分析

Abstract

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

CLC Number:

O231.4

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.

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Stability and Spectral Analysis of Nonuniform Transmission Line Equations

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