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This paper proposes an improved Linear Matrix Inequality (LMI) approach for the synthesis of Static Output Feedback (SOF) Fault-Tolerant Control (FTC). A novel slack variable is introduced into the matrix inequalities, which provides an additional degree of freedom to compute the numerical solution. Subsequently, an improved iterative algorithm is developed to obtain an optimal SOF gain with less conservativeness. In this paper, designs of the SOF gain are shown in the framework of tracking control. The nonlinear simulations of the ADMIRE aircraft are included to demonstrate the effectiveness of the proposed method.