Sliding mode control for uncertain input delay fractional order systems

A sliding mode control is developed for robust stabilization of fractional-order input-delay linear systems in presence of uncertainties and external disturbances. First, a fractional-order state predictor is used to compensate the delay in the input control. Second, a robust sliding mode control is proposed in order to stabilize the system and to thwart the effect of model uncertainties and external disturbances. The sliding mode controller is designed by considering a sliding surface defined by fractional order integral. Conditions for the existence and finite time reaching of the sliding mode in presence on bounded uncertainties and bounded external disturbances are established. Further, the stability of the closed loop system on the sliding mode is analyzed by using recent results on Lyapunov stability theory for fractional order systems. A numerical example is given to illustrate some theoretical results.