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

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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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Acknowledgements

The authors would like to thank the anonymous referees for careful reading of the manuscript and valuable suggestions.

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Authors and Affiliations

  1. School of Mathematics and Physics, Anqing Normal University, Anqing, 246052, People’s Republic of China

    Long-Sheng Liu

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  1. Long-Sheng Liu
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Communicated by Michaela Vancliff.

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Liu, LS. The General Solution to a System of Linear Coupled Quaternion Matrix Equations with an Application. Adv. Appl. Clifford Algebras 33, 48 (2023). https://doi.org/10.1007/s00006-023-01283-x

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