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In this paper, we present output feedback boundary stabilization for a classof semilinear parabolic PDEs with a boundary measurement and an actuationlocated at the same place. The method uses backstepping transformations, wherethe state and error systems are proved to be locally exponentially stable inthe $\mathbb{H}^4$ norm. The stability of the transformed systems are obtainedby constructing a strict Lyapunov function. A numerical example using theFitzHugh-Nagumo equation shows the proposed control law stabilizes the systeminto its equilibrium solution.

Output Feedback Stabilization of Semilinear Parabolic PDEs using Backstepping