Disturbance observer and Mittag-Leffler stabilization design for multi-dimensional fractional distributed parameter systems

We consider the boundary output feedback Mittag-Leffler (M-L) stabilization of a spatial multidimensional time fractional distributed parameter systems (DPSs), where the control input is actuated by Neumann boundary control input with the external disturbance. By employing the active disturbance rejection control (ADRC) approach, we design a disturbance observer consisting of two subsystems in light of the boundary output signal. The first one is utilized to channel the unknown disturbance to a stable system so that the second can observe the unknown disturbance. By employing the fractional Lyapunov method, the bounded disturbance observer can well estimate the external disturbance which means the observation error decays to zero in ??????1/2(Gamma 1). Then a disturbance-observer-based stabilizing controller is proposed to ensure the ML stability of the original system part in the closed-loop system. Finally, some simulations are included to demonstrate the theoretical results.