How to measure quantity difference between a nonlinear system of equations and its linearization?

Question

I faced such a problem. I have a nonlinear system for control synthesis and I should compare not only my controllers but also a linear version of my system to describe the legitimacy of this linearization. But it never occurred to me how to compare it in numerical. We often do it in a frequency domain for linear systems comparing bandwidth, gain, or phase margin. And we have a numerical result. But I can't do the Laplace transform (for example) because of no superposition principle being. I heard about nonlinear Fourier transform but I doubt that it could help me.