Super Twisting based Lyapunov Redesign for Uncertain Linear Delay Systems

TL;DR

This paper introduces a novel continuous Lyapunov Redesign method utilizing the Super Twisting Algorithm for robust stabilization of uncertain linear delay systems, effectively reducing chattering and ensuring asymptotic stability.

Contribution

It develops a new Lyapunov-based control approach that combines Super Twisting with Lyapunov Redesign for uncertain delay systems, enhancing robustness and stability.

Findings

Achieves asymptotic stabilization of uncertain delay systems.

Reduces chattering effects in control implementation.

Provides a systematic Lyapunov functional framework for delay compensation.

Abstract

We present a new continuous Lyapunov Redesign (LR) methodology for the robust stabilization of a class of uncertain time-delay systems that is based on the so-called Super Twisting Algorithm. The main feature of the proposed approach is that allows one to simultaneously adjust the chattering effect and achieve asymptotic stabilization of the uncertain system, which is lost when continuous approximation of the unit control is considered. At the basis of the Super Twisting based LR methodology is a class of Lyapunov-Krasovskii functionals, whose particular form of its time derivative allows one to define a delay-free sliding manifold on which some class of smooth uncertainties are compensated.