Event-triggered integral sliding mode control for fractional order T-S fuzzy systems via a fuzzy error function

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.