The General Solution to a System of Linear Coupled Quaternion Matrix Equations with an Application

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-08-09 DOI:10.1007/s00006-023-01283-x

Long-Sheng Liu

引用次数: 0

Abstract

Linear coupled matrix equations are widely utilized in applications, including stability analysis of control systems and robust control. In this paper, we establish the necessary and sufficient conditions for the consistency of the system of linear coupled matrix equations and derive an expression of the corresponding general solution (where it is solvable) over quaternion. Additionally, we investigate the necessary and sufficient conditions for the system of linear coupled matrix equations with construct to have a solution and derive a formula of its general solution (where it is solvable). Finally, an algorithm and an example were provided in order to further illustrate the primary outcomes of this paper.

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一类线性耦合四元数矩阵方程组的通解及其应用

线性耦合矩阵方程在控制系统的稳定性分析和鲁棒控制等领域有着广泛的应用。本文建立了线性耦合矩阵方程组一致性的充要条件，并导出了四元数上相应的通解（可解）的表达式。此外，我们还研究了具有构造的线性耦合矩阵方程组具有解的充要条件，并导出了其通解的一个公式（其中它是可解的）。最后，给出了一个算法和一个例子，以进一步说明本文的主要结果。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.