Stability of periodic delay systems and harmonic transfer function – I2M – Institut de Mathématique de Marseille

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Aix-Marseille Université
Institut de Mathématiques de Marseille (I2M) - UMR 7373
Site Saint-Charles : 3 place Victor Hugo, Case 19, 13331 Marseille Cedex 3
Site Luminy : Campus de Luminy - Case 907 - 13288 Marseille Cedex 9

Stability of periodic delay systems and harmonic transfer function

Laurent Baratchart
INRIA, Sophia Antipolis
https://www-sop.inria.fr/members/Laurent.Baratchart/

Date(s) : 22/03/2021 iCal
11h00

The Henry-Hale theorem says that a delay system with constant coefficients of the form y(t) = ∑ _j=1^Na_jy(t – τ_j) is exponentially stable if and only if (I –∑ _j=1^Ne^–zτ_j)^–1 is analytic in |z| > –ε for some ε > 0. We discuss an analog of this result when the a_j are periodic with Hölder-continuous derivative, saying that in this case exponential stability is equivalent to the analyticity of the so called harmonic transfer function for |z| > –ε, as a function valued in operators on L²(T) with T the unit circle. This is joint work with S. Fueyo and J.B. Pomet.

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Séminaire

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Analyse et Géométrie, Virtual event