Convergence time estimate and tuning of twisting algorithm

TL;DR

This paper provides a method to estimate convergence time and tune the gain of a twisting controller to ensure rapid stabilization of a perturbed double integrator system within a specified time frame.

Contribution

It introduces a gain tuning approach for the twisting controller that guarantees prescribed-time convergence despite disturbances.

Findings

Gain tuning method ensures convergence within desired time

Controller maintains stability under bounded disturbances

Provides explicit guidelines for gain selection

Abstract

Gain tuning is given for the twisting controller to ensure that the closed-loop trajectories of the perturbed double integrator, initialized within a bounded domain and affected by uniformly bounded disturbances, settle at the origin in prescribed time.