Event-triggered integral sliding mode control of two-time-scale systems

This paper investigates the \({H_\infty }\) $H_{\infty }$ performance of two-time-scale systems with nonlinear uncertainty and external disturbance via the event-triggered integral sliding mode control (ETISMC) strategy. To facilitate the analysis of the sliding mode surface’s reachability and the design of the event-triggered (ET) integral sliding mode controller, the \(\varepsilon \) $\epsilon$ -dependent integral sliding function with the event-triggered mechanism is constructed. Based on \({H_\infty }\) $H_{\infty }$ control theory, the integral sliding mode controller gain and the ET parameter matrix are co-designed through the solution of a set of linear matrix inequalities. The proposed event-triggered mechanism can avoid Zeno behavior. Furthermore, an adaptive ETISMC strategy is proposed to address the unknown upper bounds of uncertainty and external disturbance. Finally, the effectiveness, applicability, and advantages of the control strategies are verified by simulations and comparative analysis.