Performance and robustness analysis of nonlinear closed loop systems using μ_nl analysis: applications to nonlinear PI controllers

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 μ_nl in this paper.