Output tracking of uncertain fractional-order nonlinear systems via a novel fractional-order sliding mode approach

• In this paper a broad class of uncertain FO nonlinear systems is considered.
• A novel model FO sliding controller is designed for time-varying output tracking.
• Finite-time stability of the sliding surface and asymptotic vanishing of error signal are proved.
• The efficiency of the proposed method is shown by its application on a FO gyroscope model.

In this paper, a board class of uncertain fractional-order nonlinear systems is considered. A novel fractional-order sliding mode controller for output tracking of a time-varying reference signal is designed which can conquer the uncertainties and guarantees the asymptotic convergence of the system output toward the desired time-varying reference signal. For this purpose, an appropriate sliding surface is designed where maintaining the system’s states on this surface leads to asymptotic vanishing of error signal. Moreover, by tacking the fractional derivative of order α from the sliding surface, the convergence of system’s trajectories into the sliding surface in a finite time is proven. Finally, in order to verify the theoretical results, the proposed method is applied to a fractional-order gyroscope model and computer simulations show the efficiency of the proposed method in output tracking.