  We consider flat differential control systems for which there exist flat
outputs that are part of the state variables and study them using Jacobi bound.
We introduce a notion of saddle Jacobi bound for an ordinary differential
system of $n$ equations in $n+m$ variables. Systems with saddle Jacobi number
equal to $0$ generalize various notions of chained and diagonal systems and
form the widest class of systems admitting subsets of state variables as flat
output, for which flat parametrization may be computed without differentiating
the initial equations. We investigate apparent and intrinsic flat singularities
of such systems. As an illustration, we consider the case of a simplified
aircraft model, providing new flat outputs and showing that it is flat at all
points except possibly in stalling conditions. Finally, we present numerical
simulations showing that a feedback using those flat outputs is robust to
perturbations and can also compensate model errors, when using a more realistic
aerodynamic model.
