Conditions for the existence of a flat input

We introduce the concept of an affine flat input to a nonlinear system with a given output function. This approach can be seen as dual to the search for a flat output of a control system with given input. Our results provide a necessary and sufficient condition for the existence of a flat input in the SISO case, which also allows to construct the vector field associated to the flat input. In addition, a relation between the flat input vector field and nonlinear observer design is discussed. A population model is used to illustrate the construction of a flat input.