A remark on the boundedness and convergence properties of smooth sliding mode controllers

TL;DR

This paper provides rigorous proofs for the boundedness and convergence of smooth sliding mode controllers, addressing previous misconceptions and improving control performance by reducing chattering effects.

Contribution

It offers a rigorous theoretical analysis of smooth sliding mode controllers, correcting prior flawed conclusions in the literature.

Findings

Proves boundedness of smooth sliding mode controllers

Establishes convergence properties of the controllers

Addresses and corrects previous misconceptions in the literature

Abstract

Conventional sliding mode controllers are based on the assumption of switching control but a well-known drawback of this approach is the chattering phenomenon. To overcome the undesirable chattering effects, the discontinuity in the control law can be smoothed out in a thin boundary layer neighboring the switching surface. In this work, rigorous proofs of the boundedness and convergence properties of smooth sliding mode controllers are presented. This result corrects flawed conclusions previously reached in the literature.