This paper investigates the finite-time stabilization for a class of interconnected systems with nonlinear discontinuous interconnections in which the time-varying delay are considered. By utilizing the universal approximation ability of the fuzzy model, a unified interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy-model-based interconnected delayed system is provided. Then, in order to solve the existence of solution for the concerned system with discontinuous right-hand side, the Filippov solutions are defined based on differential inclusion theory and set-valued analysis. Furthermore, by the IT2 T–S fuzzy model approach, a delayed state feedback controller equipped with discontinuous term and time-varying delays term is proposed. According to the classical finite time stability theory and generalized Lyapunov approach, finite-time stabilization for the discontinuous interconnected delayed system is achieved, and the estimate of settling time is given. Moreover, when the detailed information of time-varying delays is unknown, the finite-time stabilization is also realized via another improved controller, which only depends upon the upper bound of time-varying delays. Finally, the proposed methodologies are illustrated by a numerical example.

中文翻译：

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通过区间类型 2 TS 模糊模型方法对不连续互连延迟系统进行有限时间稳定

本文研究了一类具有非线性不连续互连的互连系统的有限时间镇定，其中考虑了时变延迟。通过利用模糊模型的通用逼近能力，提供了一个基于统一区间类型 2 (IT2) Takagi-Sugeno (T-S) 模糊模型的互连延迟系统。然后，为了解决右侧不连续的相关系统解的存在性，基于微分包含理论和集值分析定义了Filippov解。此外，通过 IT2 T-S 模糊模型方法，提出了配备不连续项和时变延迟项的延迟状态反馈控制器。根据经典有限时间稳定性理论和广义李雅普诺夫方法，实现了不连续互连延迟系统的有限时间稳定，并给出了稳定时间的估计。此外，当时变时滞的详细信息未知时，有限时间镇定也是通过另一种改进的控制器实现的，该控制器仅依赖时变时滞的上界。最后，通过一个数值例子说明了所提出的方法。