Real spectral values coexistence and their effect on the stability of time-delay systems: Vandermonde matrices and exponential decay - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Comptes Rendus. Mathématique Year : 2020

Real spectral values coexistence and their effect on the stability of time-delay systems: Vandermonde matrices and exponential decay

Abstract

This work exploits structural properties of a class of functional Vandermonde matrices to emphasize some qualitative properties of a class of linear autonomous n−th order differential equation with forcing term consisting in the delayed dependent-variable. More precisely, it deals with the stabilizing effect of delay parameter coupled with the coexistence of the maximal number of real spectral values. The derived conditions are necessary and sufficient and represent a novelty in the litterature. Under appropriate conditions, such a configuration characterizes the spectral abscissa corresponding to the studied equation. A new stability criterion is proposed. This criterion extends recent results in factorizing quasipolynomial functions. The applicative potential of the proposed method is illustrated through the stabilization of coupled oscillators.
Fichier principal
Vignette du fichier
N_order_equation_V6-26juillet.pdf (360.95 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-02476403 , version 1 (12-02-2020)

Identifiers

Cite

Fazia Bedouhene, Islam Boussaada, Silviu-Iulian Niculescu. Real spectral values coexistence and their effect on the stability of time-delay systems: Vandermonde matrices and exponential decay. Comptes Rendus. Mathématique, 2020, 358 (9-10), pp.1011-1032. ⟨10.5802/crmath.112⟩. ⟨hal-02476403⟩
236 View
249 Download

Altmetric

Share

Gmail Facebook X LinkedIn More