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This paper is concerned with the output feedback boundary stabilization ofgeneral 1-D reaction diffusion PDEs in the presence of an arbitrarily largeinput delay. We consider the cases of Dirichlet/Neumann/Robin boundaryconditions for the both boundary control and boundary condition. The boundarymeasurement takes the form of a either Dirichlet or Neumann trace. The adoptedcontrol strategy is composed of a finite-dimensional observer estimating thefirst modes of the PDE coupled with a predictor to compensate the input delay.In this context, we show for any arbitrary value of the input delay that thecontrol strategy achieves the exponential stabilization of the closed-loopsystem, for system trajectories evaluated in $H^1$ norm (also in $L^2$ norm inthe case of a Dirichlet boundary measurement), provided the dimension of theobserver is selected large enough. The reported proof of this result requiresto perform both control design and stability analysis using simultaneously the(non-homogeneous) original version of the PDE and one of its equivalenthomogeneous representations.

Predictor-Based Output Feedback Stabilization of an Input Delayed Parabolic PDE with Boundary Measurement