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The object of this paper is to design a LMI-based fuzzy controller for a MIMO two-link robot arm using quantum evolutionary algorithms. The Takagi-Sugeno (T-S) fuzzy approach is utilized to represent the equation of motion of two-link robot arm. The stability of the fuzzy system is guaranteed by linear matrix inequality (LMI) from Lyapunov stability approach. The quantum evolutionary algorithms (QEA) are applied to find the best parameter matrix of LMI. According to QEA and LMI, the parallel distributed compensation (PDC) controller is obtained to track the state trajectory of a reference model.