Robust prescrib e d-time stabilization for fuzzy sliding mode synchronization for uncertain chaotic systems

This paper focuses on the problem of robust fuzzy sliding mode synchronization of uncertain nonlinear systems. A relevant fuzzy sliding mode control(FSMC) law is designed to force the state errors onto the specified surface. The prescribed-time boundedness (PTB) of the dynamical error is guaranteed by introducing the partitioning strategy. The chattering phenomenon, which is inherent to a conventional sliding mode control, is avoided by proper fuzzy tuning of the reaching law. The control law is deduced from the stability analysis of th closed-loop system in the sense of lyapunov. Furthermore, robustness issue is investigated and a prescribed-time property is obtained with sufficient conditions, established in terms of linear matrix inequalities (LMIs) using Lyapunov and cost functions. The results obtained show the effectiveness of the proposed control scheme and the reachability of the synchronization before the fixed time. The outcomes of this research are illustrated using computer simulations for the control problem of chaotic Chua's system, in the presence of uncertainties, which clearly reveals that FSMC is better than SMC in terms of robustness. The present proposal provides a consistent procedure to design FSMC for a general class of nonlinear systems. (c) 2021 Published by Elsevier Ltd on behalf of European Control Association.

Automated summary

This paper discusses the robust fuzzy sliding mode synchronization of uncertain nonlinear systems and designs a relevant control law to ensure the boundedness of dynamical errors within a prescribed time. The study presents sufficient conditions using stability analysis and linear matrix inequalities, demonstrating the effectiveness and reachability of the proposed control scheme. Simulation results on the chaotic Chua system validate the superiority of FSMC over SMC in terms of robustness.