论线性时延系统的稳定半径

IF 1.6 3区数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

BIT Numerical Mathematics Pub Date : 2024-01-30 DOI:10.1007/s10543-023-01006-5

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引用次数: 0

摘要

摘要线性时延微分系统稳定性半径公式中出现的指数函数用其帕代近似值来近似。这将稳定性半径公式中奇异值水平集的计算简化为特殊矩阵多项式虚特征值的计算。然后采用分段法计算稳定性半径的下限和上限。此外，还给出了四舍五入误差分析。给出了几个数值示例，以证明分段法的可行性和效率。

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On the stability radius for linear time-delay systems

Abstract

The exponential function that appears in the formula of the stability radius of linear time-delay differential systems is approximated by its Padé approximant. This reduces the computation of the level sets of singular values in the stability radius formula to the computation of imaginary eigenvalues of special matrix polynomials. Then a bisection method is used for computing lower and upper bounds on the stability radius. A rounding error analysis is presented. Several numerical examples are given to demonstrate the feasibility and efficiency of the bisection method.

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来源期刊

BIT Numerical Mathematics 数学-计算机：软件工程

CiteScore

2.90

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The journal BIT has been published since 1961. BIT publishes original research papers in the rapidly developing field of numerical analysis. The essential areas covered by BIT are development and analysis of numerical methods as well as the design and use of algorithms for scientific computing. Topics emphasized by BIT include numerical methods in approximation, linear algebra, and ordinary and partial differential equations.