High-gain fractional disturbance observer control of uncertain dynamical systems

Disturbance observer-based control allows to compensate unknown inputs, however, in most cases, requiring their integer-order differentiability. In this paper, a novel disturbance observer-based state feedback controller is proposed to compensate a more general class of fractional-, but not necessarily integer-order, differentiable unknown inputs. The proposed fractional PI-like structure yields precise conditions for feedback gain tuning. Remarkably, the resulting controller rejects non-differentiable disturbances with a smooth controller, guaranteeing robustness, an outstanding features for tracking tasks, under a prescribed practical stability regimen. A comparison to a fractional sliding mode observer is conducted via simulations to highlight the reliability of the proposed scheme.