On the Coalescence of Spectral Values and its Effect on the Stability of Time-delay Systems: Application to Active Vibration Control

Islam Boussaada (1, 2, 3) , Silviu-Iulian Niculescu (1, 3) , Sami Tliba (1) , Tomas Vyhlidal (4)

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

For linear delay-differential equations, a question of ongoing interest is to determine conditions on the equation parameters that guarantee exponential stability of solutions. Recent results have shown an unexpected link between the stable manifold and the variety characterizing multiple characteristic spectral values allowing to the right-most root assignment. In this paper, such an idea is presented and exploited in the control of active vibrations.

Keywords: Retarded functional differential equations; asymptotic stability; active vibration control; rightmost root; root assignment

Domains: Automatic; Dynamical Systems [math.DS]

Islam Boussaada, Silviu-Iulian Niculescu, Sami Tliba, Tomas Vyhlidal. On the Coalescence of Spectral Values and its Effect on the Stability of Time-delay Systems: Application to Active Vibration Control. Procedia IUTAM, 2017, 22, pp.75 - 82. ⟨10.1016/j.piutam.2017.08.011⟩. ⟨hal-01656723⟩