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DOI: 10.23952/cot.2025.53
Received November 1, 2024; Accepted February 9, 2024; Published online December 26, 2025
Abstract. Complete stability analysis of a linear time-delay system with parameters in given interval/region is not a new topic, yet a hard problem in general. In the application of the widely used methods or algorithms, even for a system with a single delay, it is necessary to use transformation, to solve nonlinear equation, to determine crossing direction of characteristic root, or to calculate Puiseux series expansion, and so on, so as to get to know properties of the characteristic quasi-polynomial required in stability analysis. This paper shows that the complete stability of a time-delay system with repeated critical imaginary roots can be carried out, directly and simply by integral evaluation and effectively, with low computational cost. It does not need any special knowledge of the quasi-polynomial such as the critical delay values and the branches of Puiseux series expansion near a repeated critical imaginary root, and it does not impose restriction on the number of delays.
How to Cite this Article:
Z. Wang, Fast stability test of linear time-delay systems with repeated critical imaginary roots simply by integral evaluation, Commun. Optim. Theory 2025 (2025) 53.