Boundary control for a class of coupled fractional reaction-diffusion systems

The problem of boundary stabilization is considered for a class of coupled fractional reaction-diffusion systems with spatially varying reactions, and a state feedback control for Robin boundary conditions is designed by the backstepping method. The original coupled system is transformed into a stable target system through a reversible integral transformation. The existence and uniqueness of the kernel function matrix is analyzed by using variable substitution and the method of successive approximations. The Mittag-Leffer stability of the close-loop system is proved by the the fractional Lyapunov direct method. Numerical simulations verify the effectiveness of the proposed method. © 2020, Editorial Department of Control Theory & Applications South China University of Technology. All right reserved.