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This work is considered with the robustness of model free adaptive control (MFAC) systems with measurement disturbances. By using statistical analysis, it is possible to investigate the influence of the measurement disturbance with statistical properties. Aiming to suppress the measurement disturbance, a modified MFAC algorithm with a decreasing gain is also proposed. Through rigorous analysis, it is shown that the modified algorithm has better robustness to measurement disturbances. The analysis is supported by simulations.