吉林大学学报（理学版）2025，Vol.63Issue(3)：765-775,11.DOI:10.13413/j.cnki.jdxblxb.2024243
一类平衡律系统的时滞反馈与稳定性分析
Delayed Feedback and Stability Analysis of a Class of Systems with Balance Laws
摘要
Abstract
We studied the stability of a class of hyperbolic systems with balance laws under delayed feedback control and the spectral analysis of the system operator by using the strictly weighted Lyapunov function method and asymptotic analysis technique.Firstly,the well-posedness of the systems was verified by using operator semigroup theory.Secondly,the exponential stability of the closed-loop system was analyzed by constructing a strictly weighted Lyapunov function.Finally,according to the asymptotic analysis technique,the asymptotic expressions of eigenvalues and eigenfunctions were obtained.The result shows that the system is exponentially stable when the feedback parameters and delayed value satisfy certain inequality constraints,and when the modulus of eigenvalues tends to positive infinity,the real part of the eigenvalues tends to a negative constant.关键词
双曲平衡律系统/时滞反馈/谱分析/指数稳定性Key words
hyperbolic systems with balance laws/delayed feedback/spectral analysis/exponential stability分类
数学引用本文复制引用
王婧雯,赵东霞,王一言,张乐..一类平衡律系统的时滞反馈与稳定性分析[J].吉林大学学报（理学版）,2025,63(3):765-775,11.基金项目
国家自然科学基金青年科学基金(批准号:12001343)和山西省自然科学基金面上项目(批准号:202403021221124). （批准号:12001343）
