Stability properties for two coupled reaction-diffusion equations

Mathieu Bajodek (1) , Hugo Lhachemi , Giorgio Valmorbida

1 L2S - Laboratoire des signaux et systèmes

This paper studies the stability of the interconnection of two reaction-diffusion equations. We focus on the case where the input and output operators of the interconnection are bounded. Using the spectral decomposition of both equations, we propose a sufficient condition to estimate the exponential stability decay rate of the closed-loop system. This stability test is proposed as constraints of a semidefinite programming. An extension of this condition is also outlined in the form of a Hurwitz criterion. The proposed stability analysis conditions are illustrated with two examples.

Keywords: Coupled PDEs; Reaction-diffusion equation; Lyapunov analysis; Spectral reduction

Domains: Automatic; Optimization and Control [math.OC]

Mathieu Bajodek, Hugo Lhachemi, Giorgio Valmorbida. Stability properties for two coupled reaction-diffusion equations. 2023. ⟨hal-03861580v2⟩