Sliding mode control for uncertain discrete-time systems based on fractional order reaching law

The design and validation of a new fractional order (FO) reaching law for uncertain discrete-time systems is studied. A sliding mode controller is subsequently constructed by adopting this law. Unlike previous works, the presented reaching law is established on the basis of the Grunwald-Letnikow FO calculus of the switching function. A high-order disturbance compensator is integrated into this reaching law to evaluate and compensate the disturbance. A rigorous theoretical analysis is given to demonstrate the superior performance of the reaching law. Results indicate that the developed method owns the ability to guarantee an O ( T n+1 ) order ultimate magnitude of the quasi-sliding mode domain. Therefore, the presented method is capable of further mitigating chattering and guaranteeing a further improvement on the control accuracy in comparison with previous reaching law methods. Moreover, sliding mode dynamics of the discrete-time system in and out the vicinities of the sliding surface is analysed in detail. Simulation results are presented to verify the feasibility and effectiveness of the developed method.