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Applications of Schur-Cohn matrix and matrix pencil methods in studying the stability of high-dimensional neutral delay differential equations

Author

Listed:
  • Ma, Jian
  • Ma, Yixue
  • Fu, Qiuxia

Abstract

This note will provide a novel method for figuring out when and where the generic high-dimensional neutral delay differential equations can keep stable. Using the Schur-Cohn matrices, matrix pencils, and generalized eigenvalues, all imaginary axis eigenvalues will be presented and the critical delays will be determined in a straightforward manner. Additionally, a simple MATLAB-based algorithm will be presented. The main contribution of this paper is that we provide a computational method for determining imaginary axis eigenvalues and minimal delay margin on general high-dimensional neutral delay differential equations with real coefficients.

Suggested Citation

  • Ma, Jian & Ma, Yixue & Fu, Qiuxia, 2026. "Applications of Schur-Cohn matrix and matrix pencil methods in studying the stability of high-dimensional neutral delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 508(C).
    • Handle: RePEc:eee:apmaco:v:508:y:2026:i:c:s0096300325003650
    DOI: 10.1016/j.amc.2025.129639
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    References listed on IDEAS

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    1. Selvam, Anjapuli Panneer & Govindaraj, Venkatesan, 2024. "Investigation of controllability and stability of fractional dynamical systems with delay in control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 89-104.
    2. Kerr, Gilbert & González-Parra, Gilberto, 2022. "Accuracy of the Laplace transform method for linear neutral delay differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 308-326.
    3. Jamilla, Cristeta & Mendoza, Renier & Mező, István, 2020. "Solutions of neutral delay differential equations using a generalized Lambert W function," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    4. Long, Shaohua & Zhang, Yu & Zhong, Shouming, 2024. "New results on the stability and stabilization for singular neutral systems with time delay," Applied Mathematics and Computation, Elsevier, vol. 473(C).
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