Control of unstable PDE with long input delay

It is well known that control of PDEs with input delay is just opening up for research. This paper presents boundary control design and stabilization for a reaction-diffusion PDE with diffusion coefficients depending on space variable and input time delay. The control design involves an interesting structure of two interconnected PDEs to transfer the input time delay into a space extension. And the stability analysis is characterized in terms of the Hi norm of the actuator state rather than the usual L2.