Consistent discretization of finite/fixed-time controllers

Abstract: The paper proposes an algorithm for a discretization (sampled-time implementation) of a homogeneous control preserving the finite-time and nearly fixed-time stability property of the original (sampling-free) system. The sampling period is assumed to be constant. Both single-input and multiple-input cases are considered. The robustness (Input-to-State Stability) of the obtained sampled-time control system is studied as well. Theoretical results are supported by numerical simulations.