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This paper studies the problem of robust control of a class of uncertain discrete-time systems. The class of uncertain systems is described by a state-space model with linear nominal parts and norm-bounded nonlinear uncertainties in the state and output equations. The authors address the problem of robust H ∞ control in which both robust stability and a prescribed H ∞ performance are required to be achieved, irrespective of the uncertainties. It has been shown that instead of the nonlinear uncertain system, one may only consider a related linear uncertain system and thus a linear static state feedback control law is designed, which is in terms of a Riccati inequality.