Stability Analysis of a More General Class of Systems with Delay-Dependent Coefficients

Chi Jin 1 Keqin Gu 2 Islam Boussaada 1, 3, 4 Silviu-Iulian Niculescu 5, 4
4 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
5 Division Systèmes - L2S
L2S - Laboratoire des signaux et systèmes : 1289
Abstract : This paper presents a systematic method to analyse the stability of systems with single delay in which the coefficient polynomials of the characteristic equation depend on the delay. Such systems often arise in, for example, life science and engineering systems. A method to analyze such systems was presented by Beretta and Kuang in a 2002 paper, but with some very restrictive assumptions. This work extends their results to the general case with the exception of some degenerate cases. It is found that a much richer behavior is possible when the restrictive assumptions are removed. The interval of interest for the delay is partitioned into subintervals so that the magnitude condition generates a fixed number of frequencies as functions of the delay within each subinterval. The crossing conditions are expressed in a general form, and a simplified derivation for the first-order derivative criterion is obtained. Illustrative examples are also presented.
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Article dans une revue
IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2019, 14, pp.1
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https://hal.archives-ouvertes.fr/hal-01957472
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Soumis le : lundi 17 décembre 2018 - 13:01:23
Dernière modification le : lundi 18 février 2019 - 11:14:02
Document(s) archivé(s) le : lundi 18 mars 2019 - 14:41:09

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Chi Jin, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu. Stability Analysis of a More General Class of Systems with Delay-Dependent Coefficients. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2019, 14, pp.1. 〈hal-01957472〉

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