A new Saturation function to convert an output constraint into an input constraint

The main result of our new method is to convert an output constraint into an input constraint for a nonlinear system. Then, standard saturated input design can be used as an anti-windup design for instance which is known to be efficient to enlarge a closed-loop system stability domain in presence of control saturations. We only address the single input single `saturated' output problem in this paper.