Rapid stabilization of a reaction-diffusion equation with distributed disturbance

International audienceIn this paper we address the problem of rapid stabilization of a reaction-diffusion equation with distributed disturbance. With the aid of the spectral decomposition of the spatial operator associated to the equation and the sign multivalued operator, which is used to reject the effects of the disturbance, we design a feedback law that exponentially stabilizes, with decay rate as large as desired, the corresponding infinite-dimensional system. The well-posedness of the resulting closed-loop system, which actually is a differential inclusion, is shown with the maximal monotone operator theory