A Schur method for robust eigenvalue assignment of second-order singular systems

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2026-02-01 Epub Date: 2025-09-17 DOI:10.1016/j.apnum.2025.09.002

Kang Hu, Huiqing Xie

引用次数: 0

Abstract

A new method for eigenvalue assignment problem of a second-order singular system is proposed via displacement-velocity-acceleration feedback. The real Schur form of a regular quadratic pencil and a robustness measurement for the closed-loop second-order system are introduced. On these grounds, a Schur method for robust eigenvalue assignment of a second-order singular system is proposed. The presented method also can be seen as an extension of the Schur method for eigenvalue assignment of a first-order system to a second-order system. However, our method directly deals with a second-order system and avoids to transform a second-order system into a first-order system. There are two open problems in the Schur method for eigenvalue assignment problem. One is how to determine the first Schur vector and another is how to order the eigenvalues in the Schur form. We provide the strategies for these two open problems, which are our main contributions. The efficiency of the proposed method is illustrated by some numerical examples.

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二阶奇异系统鲁棒特征值分配的Schur方法

提出了一种利用位移-速度-加速度反馈求解二阶奇异系统特征值分配问题的新方法。介绍了正则二次型铅笔的实Schur形式和闭环二阶系统的鲁棒性测量。在此基础上，提出了二阶奇异系统鲁棒特征值分配的Schur方法。所提出的方法也可以看作是一阶系统特征值分配的Schur方法到二阶系统的推广。然而，我们的方法直接处理二阶系统，避免了将二阶系统转化为一阶系统。特征值分配问题的Schur方法有两个开放问题。一个是如何确定第一个舒尔向量另一个是如何在舒尔形式中对特征值排序。我们为这两个开放问题提供了策略，这是我们的主要贡献。数值算例说明了该方法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.