This article considers the event‐triggered integral sliding mode control problem for fractional order T‐S fuzzy systems. A fuzzy error function and a mixed triggering threshold are proposed to design the event‐triggering mechanism, in which the fuzzy error function is used to design the triggering function. The mixed triggering threshold is composed of the time‐varying threshold with power function and the fixed one. Based on the proposed fuzzy error function, the boundedness of sliding variable errors can be guaranteed by using the time‐varying threshold with power function. Meanwhile, the fixed threshold is used to adjust the value of mixed triggering threshold near the initial time. Furthermore, a sufficient condition on the asymptotical stability for sliding motion is established and a positive internal execution time can be ensured. At last, two simulation examples are presented to illustrate the effectiveness of obtained theoretical results.

中文翻译：

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基于模糊误差函数的分数阶TS模糊系统的事件触发积分滑模控制

本文考虑了分数阶TS模糊系统的事件触发积分滑模控制问题。提出了一种模糊误差函数和混合触发阈值来设计事件触发机制，其中使用模糊误差函数来设计触发函数。混合触发阈值由具有功率函数的时变阈值和固定阈值组成。基于所提出的模糊误差函数，可以通过使用随时间变化的阈值和幂函数来保证滑动变量误差的有界性。同时，固定阈值用于在初始时间附近调整混合触发阈值。此外，建立了关于滑动运动的渐近稳定性的充分条件，并且可以确保正的内部执行时间。终于，