  This paper studies the boundary output feedback stabilization of general 1-D
reaction-diffusion PDEs in the presence of a state delay in the reaction term.
The control input applies through a Robin boundary condition while the system
output is selected as a either Dirichlet or Neumann boundary trace. The control
strategy takes the form of a finite-dimensional observer-based controller with
feedback and observer gains that are computed in order to dominate the state
delayed term. For any arbitrarily given value of the state delay, we show the
exponential stability of the resulting closed-loop system provided the order of
the observer is selected large enough.
