Fractional-order power rate type reaching law for sliding mode control of uncertain nonlinear system

This paper develops a fractional-order (FO) power rate type reaching law for sliding mode control (SMC) of nonlinear integer order systems with disturbance and uncertainty. The proposed FO power rate type reaching law, including an FO derivative function, is proven to ensure that the state trajectories achieve to the switching surface in a finite time. Most importantly, the calculation formula of the reaching time under the FO reaching law is provided, for the first time. The comparisons between the FO and IO reaching laws reveal the potential advantages of the FO reaching law. Furthermore, the criterion for stability of the sliding mode dynamics is provided by solving linear matrix inequality (LMI). Finally, simulation and experimental examples illustrate the effectiveness and advantage of the proposed control method.