Time Varying control design for small-time stabilization of Brockett's integrator

In this work, we provide new time-varying feedbacks which are stabilizing in small-time Brockett's integrator. Construction of these feedbacks is based on the uniform persistence excitation (used in [33], [34]) and the homogeneity conditions. To show high performances of the proposed feedback laws, simulations results are provided in the last section of this work.