应用数学2023，Vol.36Issue(1)：84-94,11.
一种改进的线性系统的有限时间平衡截断
A Modified Time-limited Balanced Truncation for Linear Systems
摘要
Abstract
In this paper,a modified time-limited model order reduction(MOR)method for linear systems is presented.It uses the shifted Legendre polynomials expansion vectors to perform the approximate low-rank decomposition of the Gramians for the linear systems.According to the relationship between the orthogonal polynomials and power series,the low-rank decomposition factors are obtained by a simple recurrence formula.Then,the approximate balanced system can be generated by them.After that the reduced-order models(ROMs)are obtained by truncating the states corresponding to the small approximate Hankel singular values(HSVs).Furthermore,the stability of the ROMs is discussed briefly.In the end,a numerical experiment is given to illustrate the validity of the proposed methods.关键词
模型降阶/平衡截断/Shifted Legendre多项式/有限时间/Gram矩阵Key words
Model order reduction/Balanced truncation/Shifted Legendre polynomial/Time-limited/Gramians分类
数理科学引用本文复制引用
解礼欣,肖志华,金辉..一种改进的线性系统的有限时间平衡截断[J].应用数学,2023,36(1):84-94,11.基金项目
Supported by the National Natural Science Foundation of China(61803046,51804040,11871118) （61803046,51804040,11871118）
