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<p>This paper explores the stability of quaternion matrix differential equations (QMDEs) with singular coefficients, applying integration by parts in the sense of quaternion, the scaling method, and norm estimation for the quaternion matrix exponential function. First, the integration by parts formula in the quaternion sense is established in the light of the integration by parts formula over the real field. For equations with vector functions, we deduce the Hyers-Ulam stability of linear QMDEs with singular coefficients and further provide sufficient conditions for exponential stability. Besides, we present the conditions for the Hyers-Ulam stability of the nonlinear QMDEs with singular coefficients. For equations with constant matrices, the Hyers-Ulam stability of QMDEs with singular coefficients is derived in two cases. Finally, theoretical results are illustrated with examples.</p>

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Stability to Quaternion Matrix Differential Equations with Singular Coefficients

  • 期刊论文

  • 发表日期：

    2025年7月2日

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  • Jiangnan Wang,
  • JinRong Wang,
  • Rui Liu

摘要

This paper explores the stability of quaternion matrix differential equations (QMDEs) with singular coefficients, applying integration by parts in the sense of quaternion, the scaling method, and norm estimation for the quaternion matrix exponential function. First, the integration by parts formula in the quaternion sense is established in the light of the integration by parts formula over the real field. For equations with vector functions, we deduce the Hyers-Ulam stability of linear QMDEs with singular coefficients and further provide sufficient conditions for exponential stability. Besides, we present the conditions for the Hyers-Ulam stability of the nonlinear QMDEs with singular coefficients. For equations with constant matrices, the Hyers-Ulam stability of QMDEs with singular coefficients is derived in two cases. Finally, theoretical results are illustrated with examples.