I have some nonlinear system, and i have three big question: Non-linear ODE from closed-loop system and Response 1. how correctly use such terms, like "Feedback Linearization and StateTransform Linearization" for this case, but in Mathematica they use for affine systems. There exist tranform from clearly nonlinear system to affine? 2. is there terms relate to differential geometry control? 3. is it possible to do in Mathematica a transformation to the Brunovsky form?
The example in the question you linked to is an affine system. It turns out to be not completely linearizable by state-transformation alone, but it is feedback linearizable. These techniques are for affine systems only.
FeedbackLinearize[AffineStateSpaceModel[x2'[t] == u[t] x2[t], x2[t], u[t], x2[t], t], Automatic, "LinearSystem"]
I don't follow your question.