We use Lie brackets of unbounded vector fields to consider a dissipative relation that generalizes the differential inequality which defines classic control Lyapunov functions. Under minimal regularity assumptions, we employ locally semiconcave solutions of this extended relation, called in the following degree-k control Lyapunov functions, in order to design degree-k Lyapunov feedbacks, i.e. particular discontinuous feedback laws that stabilize the underlying system to a given closed target with compact boundary, in the sample and hold sense. We also prove that this feedback construction is robust when small measurement errors and external disturbances occur.

我们使用无界矢量场的李括号来考虑耗散关系，该耗散关系概括了定义经典控制Lyapunov函数的微分不等式。在最小规律性假设下，我们采用这种扩展关系的局部半凹解，在以下的k级控制Lyapunov函数中进行调用，以设计k级Lyapunov反馈，即特定的不连续反馈定律，以将基础系统稳定到给定的封闭状态在采样和保持意义上具有紧凑边界的目标。我们还证明，当出现较小的测量误差和外部干扰时，这种反馈结构是可靠的。