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

Florian Monteghetti (1) , G Haine (2) , D Matignon (2)

1 ONERA - The French Aerospace Lab [Toulouse]
2 ISAE-SUPAERO - Institut Supérieur de l'Aéronautique et de l'Espace

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.

Mots clés: Systems with time-delays; stability of delay systems; fractional-order systems; Lyapunov methods; semigroup and operator theory; diffusive representation

Domaines: Equations aux dérivées partielles [math.AP]

Florian Monteghetti, G Haine, D Matignon. Stability of Linear Fractional Differential Equations with Delays: a coupled Parabolic-Hyperbolic PDEs formulation. 20th World Congress of the International Federation of Automatic Control (IFAC WC), Jul 2017, Toulouse, France. ⟨hal-01618048⟩