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 for $n$ equations in $n+m$ variables. Systems with saddle Jacobi number 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.

翻译：我们考虑一类存在状态变量子集作为平坦输出的平坦微分控制系统，并利用雅可比界对其进行研究。针对含n个方程与n+m个变量的常微分系统，引入鞍型雅可比界概念。具有鞍型雅可比数的系统将多种链式系统与对角系统概念泛化，构成允许状态变量子集作为平坦输出的最宽泛系统类别，其平坦参数化可通过无微分初始方程的方式计算。我们探讨此类系统的表观奇点与内禀平坦奇点。以简化飞机模型为例，给出新型平坦输出，并证明除失速条件外所有点均具有平坦性。最后通过数值仿真表明：采用这些平坦输出的反馈控制既能抵抗扰动，在使用更真实的气动模型时还可补偿建模误差。