This article considers the reachable set estimation problem and membership function dependent H∞H_\infty performance analysis for a class of fuzzy Markov jump systems (FMJSs) with mode-dependent time-varying delays and bounded external disturbances via sampled-data control. First, mode-dependent sampled-data control for the FMJS is designed using the Takagi–Sugeno (T–S) fuzzy method. Then, a novel stochastic Lyapunov–Krasovskii functional (LKF) is constructed in mode-dependent augmented form by taking full advantage of the variable characteristics related to the actual sampling pattern. At the same time, a membership function dependent H∞H_\infty performance index is introduced for the first time to attenuate the impact of disturbances on the closed-loop FMJS. Based on the novel H∞H_\infty performance index and LKF, new delay-dependent conditions are derived in the framework of linear matrix inequalities to ensure stochastic stability of the closed-loop system and its reachable set is bounded by an ellipsoid in the presence of bounded disturbances. Finally, two illustrated application problems validate theoretical results with less conservatism in the sense of enlarging the sampling period and minimizing the disturbance attenuation level.

中文翻译：

---

通过隶属函数相关 H 性能实现时变时滞 T 模糊马尔可夫跳跃系统的可达集估计


本文考虑了一类模糊马尔可夫跳跃系统 (FMJS) 的可达集估计问题和隶属函数相关的 H∞H_\infty 性能分析，该系统具有依赖于模式的时变延迟和通过采样数据控制的有界外部干扰。首先，使用 Takagi–Sugeno (T–S) 模糊方法设计 FMJS 的模式相关采样数据控制。然后，通过充分利用与实际采样模式相关的变量特征，以模式相关的增强形式构造一种新颖的随机 Lyapunov-Krasovskii 泛函（LKF）。同时，首次引入了依赖于隶属函数的H∞H_\infty性能指标，以减弱扰动对闭环FMJS的影响。基于新的H∞H_\infty性能指标和LKF，在线性矩阵不等式的框架下推导了新的时滞相关条件，以确保闭环系统的随机稳定性，并且其可达集在存在的情况下以椭球为界的有界扰动。最后，两个说明的应用问题验证了理论结果，在扩大采样周期和最小化干扰衰减水平方面具有较少的保守性。