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This paper presents a method to design a predictive controller for a single Inverted Pendulum (SIP) system. The design goal is to balance the pendulum in the inverted position in the presence of parameter variations and measurement white noise Using linearization technique, the model of SIP system is transformed to a linear polytopic system. Since we need to estimation of states, a new robust model predictive control (RMPC) strategy is developed for this system with considering white measurement noise. Simulation results are presented to show the robustness of the closed-loop system against parameter variations and measurement white noise.