Stabilization of reaction-diffusion equations with state delay using boundary control input

This study analyses a stabilization method for reaction-diffusion equations with state delay using boundary control input. The proposed control strategy is based on the backstepping method, wherein the controlled system is transformed into a target system. The objective of this study is to show that the conventional transformation, which was proposed for undelayed reaction-diffusion equations, can still provide a stabilizing boundary controller for a special class of delayed equations.