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This paper addresses stabilization problem with decay rate analysis for discrete-time linear systems subject to actuator saturation. The saturation-dependent Lyapunov function is exploited to propose new stability conditions by introducing additional slack variables. Especially, elimination Lemma is used to show the stable property of one slack variable. If the stable slack variable is specified a priori by a systematic and simple approach, via a cone complementarity approach , a state feedback controller is then designed by using LMI-based optimization algorithm which guarantees an upper bound on the decay rate of the system. The simulation results illustrate the effectiveness of the proposed methods.