A frequency-sweeping framework for stability analysis of time-delay systems

Xu-Guang Li 1 Silviu-Iulian Niculescu 2 Arben Cela 3 Lu Zhang 4 Xu Li 1
2 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
Abstract : For time-delay systems, the asymptotic behavior analysis of the critical imaginary roots w.r.t. the infinitely many critical delays is an open problem. In order to find a general solution, we will exploit the link between the asymptotic behavior of critical imaginary roots and the asymptotic behavior of frequency-sweeping curves, from a new analytic curve perspective. As a consequence, we will establish a frequency-sweeping framework with three main results: (1) A finer (regularity-singularity) classification for time-delay systems will be obtained. (2) The general invariance property will be proved and hence the asymptotic behavior of the critical imaginary roots w.r.t. the infinitely many critical delays can be adequately studied. (3) The complete stability problem can be fully solved. Moreover, the frequency-sweeping framework is extended to cover a broader class of time-delay systems. Finally, the geometric insights of frequency-sweeping curves are investigated. Consequently, some deeper properties on the asymptotic behavior of time-delay systems and the link to frequency-sweeping curves are found.
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https://hal-centralesupelec.archives-ouvertes.fr/hal-01431725
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Submitted on : Wednesday, January 11, 2017 - 11:05:21 AM
Last modification on : Tuesday, June 4, 2019 - 11:08:03 AM

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Xu-Guang Li, Silviu-Iulian Niculescu, Arben Cela, Lu Zhang, Xu Li. A frequency-sweeping framework for stability analysis of time-delay systems. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2017, 64, pp.16. ⟨10.1109/TAC.2016.2633533⟩. ⟨hal-01431725⟩

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