Finite-time stabilization of fractional-order systems with model uncertainties and external disturbances

In this paper, a fractional-order sliding mode controller is proposed to realize the finite-time stabilization of fractional order (FO) system. The FO systems are perturbed by model uncertainties and external disturbances. First, a new fractional non-singular terminal sliding surface with desired dynamics is proposed. Subsequently, on the basis of Lyapunov function and finite-time control theory, a robust control law is introduced to guarantee the occurrence of the sliding motion in a given time. It demonstrates that reaching and sliding phases both are finite-time convergent. Finally, an example is provided to illustrate the effectiveness of the proposed method.