Impedance response of a linear system is independent of the perturbation amplitude?
The response of a linear system does not depend on the perturbation amplitude.

That's the definition of what it means to be a linear system.


  If I have a non-linear system,


... then you can't expect a result specified to apply to a linear system to apply to your system.

In the real world, just about all systems are non-linear, but often it is useful to approximate their behavior with a linear model.