Robust feedback stabilization by means of Lyapunov-like functions determined by Lie brackets

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 assump- tions, 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.