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

2008/02/21 by Wallace Moreira Bessa, Bessa, Wallace Moreira
Engineering · Mathematics · #93C10 #93C40 #Advanced Mathematical Physics Problems #FOS: Mathematics #Numerical methods for differential equations #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.0802.2978

openalex publication_date 2008/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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