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Stability of Linear Fractional Differential Equations with Delays: a coupled Parabolic-Hyperbolic PDEs formulation

Monteghetti, Florian and Haine, Ghislain and Matignon, Denis Stability of Linear Fractional Differential Equations with Delays: a coupled Parabolic-Hyperbolic PDEs formulation. (2017) In: The 20th World Congress of The International Federation of Automatic Control (IFAC 2017), 9 July 2017 - 14 July 2017 (Toulouse, France).

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Official URL: https://doi.org/10.1016/j.ifacol.2017.08.1966

Abstract

Fractional differential equations with delays are ubiquitous in physical systems, a recent example being time-domain impedance boundary conditions in aeroacoustics. This work focuses on the derivation of delay-independent stability conditions by relying on infinite-dimensional realisations of both the delay (transport equation, hyperbolic) and the fractional derivative (diffusive representation, parabolic). The stability of the coupled parabolic-hyperbolic PDE is studied using straightforward energy methods. The main result applies to the vector-valued case. As a numerical illustration, an eigenvalue approach to the stability of fractional delay systems is presented.

Item Type:Conference or Workshop Item (Paper)
Additional Information:volume 50, n°1.
Audience (journal):International peer-reviewed journal
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
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Deposited By: Ghislain Haine
Deposited On:18 Oct 2017 14:23

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