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Elsewhere, an approach based on the incremental norm was proposed for formalizing nonlinear performance as a well posed optimization framework. Many realistic specifications can be considered in this framework. The underlying philosophy is close to the H∞ approach proposed by Zames in 1981. In this paper, we illustrate the strong interest of this approach for analyzing nonlinear PID control of linear time invariant (LTI) systems on an example (a nonlinearity is introduced for improving noise filtering). This analysis is based on the extension of the μ analysis (LTI robustness analysis) to nonlinear systems, referred to as μnl in this paper.