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.

本文重点研究不确定非线性系统的鲁棒模糊滑模同步问题。设计了相关的模糊滑模控制（FSMC）定律，以将状态误差强行施加到指定的表面上。通过引入分区策略，可以保证动态误差的规定时间有界性（PTB）。通过对到达定律进行适当的模糊调整，可以避免传统的滑模控制所固有的颤动现象。控制律是从lyapunov的意义上从闭环系统的稳定性分析中得出的。此外，研究了鲁棒性问题，并使用Lyapunov和成本函数根据线性矩阵不等式（LMI）建立了具有充分条件的规定时间属性。获得的结果表明了所提出的控制方案的有效性以及在固定时间之前同步的可达性。在存在不确定性的情况下，使用计算机仿真对混沌Chua系统的控制问题进行了说明，表明了本研究的结果，这清楚地表明，就鲁棒性而言，FSMC优于SMC。本提议提供了用于为一类通用非线性系统设计FSMC的一致程序。