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Stability analysis of time-delay systems in the parametric space

Abstract : This paper presents a novel method for stability analysis of a wide class of linear, time-delay systems (TDS), including retarded non-neutral ones, as well as those incorporating incommensurate and distributed delays. The proposed method is based on frequency domain analysis and the application of Rouché's theorem. Given a parametrized TDS, and some parametric point for which the number of unstable poles is known, the proposed method is capable of identifying the maximum surrounding region in the parametric space for which the number of unstable poles remains invariant. First, a procedure for investigating stability along a line is developed. Then, the results are extended by the application of Hölder's inequality to investigating stability within a region. Contrary to existing approaches, the proposed method is uniformly applicable to parameters of different types (delays, distributed delay limits, time constants, etc.). Efficacy of the proposed method is demonstrated using illustrative examples.
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https://hal.archives-ouvertes.fr/hal-03184836
Contributor : Rachid Malti <>
Submitted on : Monday, March 29, 2021 - 8:05:40 PM
Last modification on : Wednesday, March 31, 2021 - 3:23:58 AM

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  • HAL Id : hal-03184836, version 1

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Vukan Turkulov, Milan Rapaić, Rachid Malti. Stability analysis of time-delay systems in the parametric space. 2021. ⟨hal-03184836⟩

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