Multivariable Super-Twisting Algorithm for Systems with Uncertain Input Matrix and Perturbations

TL;DR

This paper introduces a multivariable Super-Twisting control algorithm designed to handle systems with time-varying uncertainties in the input matrix and perturbations, ensuring robust finite-time stability.

Contribution

It presents a Lyapunov-based design method for a generalized Super-Twisting algorithm that guarantees stability despite uncertain control matrices and perturbations.

Findings

Ensures global finite-time stability under uncertainties

Provides a systematic gain selection procedure

Demonstrates effectiveness through robot simulations

Abstract

This paper proposes a Lyapunov approach to the design of a multivariable generalized Super-Twisting algorithm (MGSTA), which is able to control a system with perturbations and uncertain control matrix, both depending on time and the system states. The presented procedure shows that, under reasonable assumptions for the uncertainties, it is always possible to find a set of constant gains for the MGSTA in order to ensure global and robust finite-time stability of the system's outputs. Simulation results on an omnidirectional mobile robot illustrate the performance of the MGSTA.