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Reversals in stability of linear time-delay systems A finer characterization

Abstract : In most of the numerical examples of time-delay systems proposed in the literature, the number of unstable characteristic roots remains positive before and after a multiple critical imaginary root (CIR) appears (as the delay, seen as a parameter, increases). This fact may lead to some misunderstandings (i) A multiple CIR may at most affect the instability degree; (ii) It cannot cause any stability reversals (stability transitions from instability to stability). As far as we know, whether the appearance of a multiple CIR can induce stability is still unclear (in fact, when a CIR generates a stability reversal has not been specifically investigated). In this paper, we provide a finer analysis of stability reversals and some new insights into the classification the link between the multiplicity of a CIR and the asymptotic behavior with the stabilizing effect. Based on these results, we present an example illustrating that a multiple CIR's asymptotic behavior is able to cause a stability reversal. To the best of the authors’ knowledge, such an example is a novelty in the literature on time-delay systems.
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Submitted on : Wednesday, October 23, 2019 - 12:59:28 PM
Last modification on : Thursday, January 20, 2022 - 5:29:52 PM

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Xu Li, Jian-Chang Liu, Xu-Guang Li, Silviu-Iulian Niculescu, Arben Cela. Reversals in stability of linear time-delay systems A finer characterization. Automatica, Elsevier, 2019, 108, pp.108479. ⟨10.1016/j.automatica.2019.06.031⟩. ⟨hal-02328850⟩

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