  This paper is concerned with the output feedback stabilization of a
reaction-diffusion equation by means of bounded control inputs in the presence
of saturations. Using a finite-dimensional controller composed of an observer
coupled with a finite-dimensional state-feedback, we derive a set of conditions
ensuring the stability of the closed-loop plant while estimating the associated
domain of attraction in the presence of saturations. This set of conditions is
shown to be always feasible for an order of the observer selected large enough.
The stability analysis relies on Lyapunov functionals along with a generalized
sector condition classically used to study the stability of linear
finite-dimensional plants in the presence of saturations.
