Abstract
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.
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