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) , Tomas Vyhlidal (5)

1 L2S - Laboratoire des signaux et systèmes
2 IPSA - Institut Polytechnique des Sciences Avancées
3 DISCO - Dynamical Interconnected Systems in COmplex Environments
4 Anadolu [Turkey]
5 CTU - Czech Technical University in Prague

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

Domains: Engineering Sciences [physics]; Automatic; Mathematics [math]; Dynamical Systems [math.DS]

Islam Boussaada, Sami Tliba, Silviu-Iulian Niculescu, Hakki Ulaş Unal, Tomas Vyhlidal. 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, 2018, 542, pp.589-604. ⟨10.1016/j.laa.2017.11.022⟩. ⟨hal-01657659⟩