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This paper proposes a multi-objective H2/H ∞ maximum power tracking control of a variable speed wind turbine to minimize the H2 tracking error and ensure the H ∞ model reference-tracking performance, simultaneously. The optimal condition is obtained via a boost converter use, which adapts the load impedance to the wind turbine generator. Thus, based on the fuzzy T-S model, a multi-objective Maximum Power Point Tracking (MPPT) controller is developed, ensuring maximum power transfer, despite wind speed variation and system uncertainty. To specify the optimal trajectory to follow, a TS reference model is proposed taking as input the optimal rectified DC current. The conditions of stability and stabilization are expressed in terms of linear matrix inequality (LMI) for uncertain and disturbed T-S models leading to determining the controller gains. Finally, an example of MPP tracking applied to a Wind Energy Conversion System (WECS) illustrates the effectiveness of the proposed fuzzy control law. [ABSTRACT FROM AUTHOR]