Abstract The present study focuses on designing the integral sliding-mode control (ISMC) for generalized Takagi–Sugeno (T–S) fuzzy singular stochastic systems by involving the Markovian jump type of system parameters. Distinct to the existing works, the present paper concerns about the derivation of sufficient conditions that ensure the global stability of considered T–S fuzzy stochastic singular Markovian jump systems with matched/mismatched uncertainties under fuzzy-based ISMC. In this regard, an improved fuzzy integral sliding manifold function with mode-dependent derivative-term coefficient is proposed where the matched uncertainties become unnecessary and the mismatched uncertainties have been disintegrated during the sliding mode phase. Based on Lyapunov stability theory, a suitable Lyapunov functional candidate by involving the information about the membership functions is constructed with singular and P-type matrices, the stochastic admissibility of corresponding sliding mode dynamics are derived. To proven the effectiveness of the proposed method, a physical experimental problem on cart and pendulum is adapted and simulated via the derived theoretical results and the corresponding results are provided.

中文翻译：

---

T-S模糊描述符系统的积分滑模控制

摘要 本研究的重点是通过涉及马尔可夫跳跃类型的系统参数来设计广义 Takagi-Sugeno (T-S) 模糊奇异随机系统的积分滑模控制 (ISMC)。与现有工作不同，本文关注充分条件的推导，以确保在基于模糊的 ISMC 下具有匹配/不匹配不确定性的 T-S 模糊随机奇异马尔可夫跳跃系统的全局稳定性。在这方面，提出了一种具有模态相关导数项系数的改进模糊积分滑动流形函数，其中匹配的不确定性变得不必要，并且不匹配的不确定性在滑模阶段已被分解。基于李雅普诺夫稳定性理论，用奇异矩阵和P型矩阵构造一个合适的Lyapunov泛函候选，通过涉及隶属函数的信息，推导出相应滑模动力学的随机容许性。为了证明所提出方法的有效性，通过推导的理论结果对推车和摆锤的物理实验问题进行了调整和模拟，并提供了相应的结果。