In this paper, two new local measures of non-linearity are introduced to quantify the sensitivity of controller stability and performance for linear controllers operating on a non-linear plant. The measure quantifies the departures from optimality of locally linear quadratic regulators. The main difference between this technique and all other techniques presented in the literature is that the analysis can be used directly in the control design step. If a linear controller can be shown to operate as intended, despite the non-linearity, then a practitioner can apply a linear controller to the non-linear systems with the guarantee that a certain degree of performance can be assured, at the design step.