Further remarks on the effect of multiple spectral values on the dynamics of time-delay systems. Application to the control of a mechanical system

Islam Boussaada; Sami Tliba; Silviu-Iulian Niculescu; Hakki Ulaş Unal; Tomáš Vyhlídal

Further remarks on the effect of multiple spectral values on the dynamics of time-delay systems. Application to the control of a mechanical system

Islam Boussaada ^{1, 2, 3} Sami Tliba ¹ Silviu-Iulian Niculescu ^{1, 3} Hakki Ulaş Unal ⁴ Tomáš Vyhlídal ⁵

1 L2S - Laboratoire des signaux et systèmes

2 IPSA - Institut Polytechnique des Sciences Avancées

3 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

4 Anadolu [Turkey]

5 CTU - Czech Technical University in Prague

Abstract : A question of ongoing interest for linear Time-delay systems is to determine conditions on the equation parameters that guarantee the exponential stability of solutions. In recent works a new interesting property of time-delay systems was emphasized. As a matter of fact, the multiple spectral values for time-delay systems was characterized by using a Birkhoff/Vandermonde-based approach. Then, a multiplicity induced stability criteria exhibited for reduced order systems; scalar delay-equations and a special class of second order systems. This work, further explores such a criteria and shows their applicability to the control of a mechanical system.

Keywords : Stability frequency-domain approach Vibration control Time-Delay Control design

Document type :

Journal articles

Domain :

Engineering Sciences [physics] / Automatic

Mathematics [math] / Dynamical Systems [math.DS]

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https://hal-centralesupelec.archives-ouvertes.fr/hal-01657659
Contributor : Islam Boussaada <>
Submitted on : Wednesday, January 10, 2018 - 9:01:21 AM
Last modification on : Tuesday, June 4, 2019 - 11:08:06 AM
Long-term archiving on : Wednesday, May 23, 2018 - 5:48:42 PM

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Further remarks on the effect of multiple spectral values on the dynamics of time-delay systems. Application to the control of a mechanical system

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