Implicit-Euler Discretization with Twisting Algorithm via Immersion & Invariance Approach

Abstract

This paper presents a time-discretization methodology for designing a control law for stabilizing a continuous plant. It relies on the concept of immersion and invariance principle with implicit-Euler discretization of Twisting algorithm. The multi-valuedness of the signum function on the off-the-manifold is fully utilized by this discretization. By eliminating numerical chattering in the control input and system output, the resulting controller ensures a smooth stabilization of the off-the-manifold. Additionally, the exogenous disturbance that is currently affecting the system is diminished by a factor of h (h is the sampling interval) as well. The efficacy of proposed technique are shown through comparative study in the simulations. Copyright © 2023 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)