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This paper studies the design of a robust discrete-time sliding-mode control (DT-SMC) for a high precision electrohydraulic actuator (EHA) system. Nonlinear friction in the hydraulic actuator can greatly influence the performance and accuracy of the hydraulic actuators, and it is difficult to accurately model the nonlinear friction characteristics. In this paper, it is proposed to characterize the frictions as an uncertainty in the system matrices. Indeed, the effects of variations of the nonlinear friction coefficients are considered as norm-bounded uncertainties that span a bounded region to cover a wide range of the real actuator friction. For such a discrete-time dynamic model, for the EHA system with system uncertainty matrices and a nonlinear term, a sufficient condition for existence of stable sliding surfaces is proposed by using the linear matrix inequality approach. Based on this existence condition, a DT-SMC is developed such that the reaching motion satisfies the discrete-time sliding mode reaching condition for uncertain systems. Simulation and experimental studies on the EHA system illustrate the effectiveness and applicability of the proposed method.