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

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.
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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. Linear Algebra and its Applications, Elsevier, 2018, 542, pp.589-604. ⟨10.1016/j.laa.2017.11.022⟩. ⟨hal-01657659⟩

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