Stabilization and Stability Robustness of Coupled Non-Constant Parameter Time Fractional PDEs

This paper considers observer-based output feedback stabilization and stability robustness against small diffusivity perturbations of coupled time fractional partial differential equations (PDEs) with space-dependent (non-constant) parameters. Herein, the plant is equipped with the only available measurement at x=0 and actuation at x=1 . By backstepping transformation, the well-posedness of the kernel matrix PDE and the observer gains are obtained. Then an output feedback controller is introduced and the Mittag-Leffler stability of the closed-loop system is proved by the fractional Lyapunov method. Robustness analysis of diffusion coefficients uncertainty (with a small perturbation in the diffusion coefficient) is also provided. The output feedback stabilization of the closed-loop system is tested by a numerical example.