In this article, we investigate the problems of robust exponential stabilization in mean square and $\mathcal {H}_{\infty }$ -based integral sliding mode controller design for uncertain stochastic Takagi–Sugeno (T-S) fuzzy switched time-delay systems with both matched and unmatched uncertainties under synchronous switching and asynchronous switching, respectively. In these systems, the control input is dependent on a switching signal. Under synchronous switching and asynchronous switching, sufficient conditions are developed to guarantee that the resulting closed-loop systems are robustly exponentially stable in mean square with a prescribed $\mathcal {H}_{\infty }$ -performance, respectively. The integral sliding mode surfaces and the sliding mode controllers are designed for the underlying systems under synchronous switching and asynchronous switching, respectively. By two examples stemming from the mass–spring–damper model and the single-link robot arm model under stochastic perturbation, the effectiveness of the results obtained is verified.

中文翻译：

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基于积分滑模策略的不确定随机模糊切换时滞系统的鲁棒 $\mathcal {H}_{\infty }$-Based Control

在本文中，我们研究了均方和稳健指数稳定的问题$\mathcal {H}_{\infty }$ 基于积分滑模控制器设计，用于在同步切换和异步切换下分别具有匹配和不匹配不确定性的不确定随机高木-菅野 (TS) 模糊切换时滞系统。在这些系统中，控制输入取决于开关信号。在同步切换和异步切换下，开发了充分的条件来保证所得到的闭环系统在均方上是稳健指数稳定的，具有规定的$\mathcal {H}_{\infty }$ -性能，分别。积分滑模面和滑模控制器分别针对同步切换和异步切换下的底层系统设计。通过质量-弹簧-阻尼器模型和随机扰动下的单连杆机械臂模型的两个例子，验证了所得结果的有效性。