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The H∞ control problem for discrete-time nonlinear systems with bounded controllers is considered. Applying the receding horizon method for a game problem, a state feedback control law is proposed which imposes a prescribed level of disturbance attenuation with internal stability in a larger domain of the state space than by other methods existing in the literature. Under some further conditions a global solution for the problem is also given. The proposed method cannot only be applied to cases amenable to solution by other methods but also to cases for which the linearisation technique does not work. The application of the method is illustrated by an example.