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

Jian Ma, Yixue Ma and Qiuxia Fu

Applied Mathematics and Computation, 2026, vol. 508, issue C

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.

Keywords: Neutral delay differential equations; Schur-Cohn matrix; Matrix pencils; Stability; Eigenvalues (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:508:y:2026:i:c:s0096300325003650

DOI: 10.1016/j.amc.2025.129639

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