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This paper proposes a robust nonlinear current controller that deals with the problem of the stator current control of a six-phase induction motor drive. The current control is performed by using a state-space representation of the system, explicitly considering the unmeasurable states, uncertainties and external disturbances. To estimate these latter effectively, a time delay estimation technique is used. The proposed control architecture consists of inner and outer loops. The inner current control loop is based on a robust discrete-time sliding mode controller combined with a time delay estimation method. As said before, the objective of the time delay estimation is to reconstruct the unmeasurable states and uncertainties, while the sliding mode aims is to suppress the estimation error, to ensure robustness and finite-time convergence of the stator currents to their desired references. The outer loop is based on a proportional-integral controller to control the speed. The stability of the current closed-loop system is proven by establishing sufficient conditions on the switching gains. Experimental work has been conducted to verify the performance and the effectiveness of the proposed robust control scheme for a six-phase induction motor drive. The results obtained have shown that the proposed method allows good performances in terms of current tracking, in their corresponding planes.