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A stabilizing output feedback model predictive control algorithm is proposed for linear systems with input constraints. Dual mode control strategy is adopted: the state observer, linear feedback controller and terminal constraint set are pre-computed; if the state is contained in terminal constraint set, linear feedback controller is used; otherwise a linear control structure with free vector is used, and control law can be obtained by solving an Second Order Cone Programming (SOCP) problem. The system with bounded disturbance is considered and bounded stability is shown. Simulations results show the effectiveness of the control algorithm.