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

IF 1.1 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras 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

Advances in Applied Clifford Algebras 数学-物理：数学物理

CiteScore

2.20

自引率

13.30%

发文量

审稿时长

3 months

期刊介绍： Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.