Asymptotic stability of linear conservative systems when coupled with diffusive systems
Denis Matignon, Christophe Prieur (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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In this paper we study linear conservative systems of finite dimension coupled with an infinite dimensional system of diffusive type. Computing the time-derivative of an appropriate energy functional along the solutions helps us to prove the well-posedness of the system and a stability property. But in order to prove asymptotic stability we need to apply a sufficient spectral condition. We also illustrate the sharpness of this condition by exhibiting some systems for which we do not...