Consistent discretization of finite/fixed-time controllers

TL;DR

This paper introduces an algorithm for discretizing homogeneous finite/fixed-time controllers that maintains their stability properties under constant sampling periods, with robustness analysis and numerical validation.

Contribution

It presents a novel discretization method that preserves finite-time and fixed-time stability in sampled systems, extending previous continuous-time control approaches.

Findings

The discretization preserves stability properties in sampled systems.

The method is applicable to both single-input and multi-input controllers.

Numerical simulations confirm theoretical stability and robustness results.

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.