This study presents a comprehensive analysis of the convergence properties of a positive position feedback (PPF) control system applied to a single-degree-of-freedom system, utilizing perturbation techniques. Through the application of the multiple-scale perturbation method, approximate solutions for the system dynamics are derived, revealing insights into amplitude reduction and convergence behavior under PPF control. The findings demonstrate the efficacy of the perturbation approach in accurately predicting the exponential decay of controlled responses.