This article analyzes the integral sliding mode control (ISMC) problem for the nonlinear stochastic system by employing the fuzzy approach. Firstly, the Takagi-Sugeno (T-S) fuzzy stochastic model with unknown nonlinear function and external disturbance has been developed. Based on the fuzzy model, an observer-based integral sliding mode fuzzy controller is derived under the event-triggered scheme (ETS). The Lyapunov-Krasovskii functionals (LKFs) involving double and triple integral terms are considered and evaluated by applying Writinger inequality lemma and reciprocally convex combination lemma. With the help of matrix's singular value decomposition lemma, the stability conditions have been derived which is in terms of linear matrix inequalities (LMIs) and this can be solved by MATLAB LMI toolbox. Two numerical examples are provided to demonstrate the usefulness of our theoretical conclusions.

中文翻译：

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Takagi-Sugeno模糊随机系统的事件触发积分滑模控制

本文采用模糊方法分析非线性随机系统的积分滑模控制（ISMC）问题。首先，建立了具有未知非线性函数和外部干扰的Takagi-Sugeno（TS）模糊随机模型。在模糊模型的基础上，推导出事件触发方案(ETS)下基于观测器的积分滑模模糊控制器。Lyapunov-Krasovskii 泛函 (LKF) 涉及双重和三重积分项，通过应用Writer 不等式引理和倒凸组合引理来考虑和评估。借助矩阵的奇异值分解引理，推导出了线性矩阵不等式（LMI）的稳定性条件，这可以通过MATLAB LMI工具箱解决。