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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基于区间2型T__模糊模型方法的不连续互联时滞系统的有限时间稳定


本文研究了一类考虑时变延迟的非线性不连续互连系统的有限时间稳定性。利用模糊模型的万能逼近能力，提出了一种基于统一区间2型(IT2) Takagi-Sugeno (TS)模糊模型的互联时滞系统。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 TS模糊模型方法，提出了一种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Lyapunov方法，实现了间断互联时滞系统的有限时间稳定，并给出了稳定时间的估计。此外，当时变延迟的详细信息未知时，还可以通过另一种改进的控制器来实现有限时间稳定，该控制器仅依赖于时变延迟的上限。最后，通过数值例子说明了所提出的方法。