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Minimum achievable output variance (MAOV) is a common benchmark for control performance assessment. Finding the MAOV of proportional–integral–derivative (PID) control systems is computationally expensive due to the inherent non-convexity of the associated optimization problem. We present in this paper a new framework for computing the MAOV of PID control systems. The problem of estimating the MAOV of a PID control system is novelly formulated as a convex program with an additional non-convex constraint. The non-convex constraint is linearized and handled by the penalty approach. Based on this, a low-complexity algorithm, which relies on the iterative convex programming technique, is developed to solve the MAOV problem. The new algorithm is proved to be convergent. We show via numerical examples that the new approach yields close-to-optimal solutions that are better than (or as good as …