Backstepping design for a class of coupled parabolic PDEs with spatially varying coefficient

In this paper, we concentrate on the state feedback stabilization of a class of coupled parabolic partial differential equations with space dependent diffusion coefficients. To stabilize the system, we design a state feedback controller using the backstepping technique. Namely, we convert the original system into a stable desired system called the target system to obtain a backstepping feedback controller. We prove that the feedback controller causes the main system to be exponential stable. Also, the numerical simulations show that validity and efficiency of theoretical results.