Stability properties for two coupled reaction-diffusion equations

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 an example of two reaction-diffusion equations with constant couplings terms. Copyright (c) 2023 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)