Linear time invariant (LTI) systems are a staple of physics. They appear in many situations. But how do you know a system is a LTI?
In particular, if you are provided with a black box which responds to some input I(t) yielding some output O(t), and you do not know I(t) or O(t) for t=t0, can you determine whether the black box is an LTI? (You may use your observations to craft later inputs: I(t) may depend on O(x) for x on [t0, t) )
If it cannot be done, are there theorems which provide bounds on the nonlinear effects?