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This paper presents a H∞ methodology design of a linearized polytopic model for an induction motor. Output feedback controller is designed to provide non saturate control and minimum tracking error of both rotor speed and flux norm when the model is subjected to parameter variation. The nominal plant of a fourth order polytopic model is used to implement an LMI-based H∞ approach. Numerical simulation results are reported to show the effectiveness of the proposed controller in presence of deviation parameter.