The paper presents an example how a nonlinear missile model controlled by a nonlinear dynamic inversion (NDI) based feedback structure can be approximated by a linear fractional representation (LFR). The aim is to obtain an LFR of suitable complexity for applying LFT-based robust stability analysis. The first step is the transformation of the nonlinear closed loop into a quasi linear parameter varying (LPV) system via a method called function substitution. In the second step the nonlinear dependencies in the quasi-LPV model, which are not rational in the parameters, are approximated using polynomial fitting based on '1-regularized least squares. Using this approach an almost Pareto front between the accuracy and complexity of the resulting LFR can be easily obtained. The quality of the closed loop LFR is assessed by using Monte-Carlo simulations.