Event-Triggered Adaptive Sliding Mode Control for Interval Type-2 T-S Fuzzy Systems with Time-Varying Delay

Abstract This work proposes an event-triggered adaptive sliding mode control strategy for nonlinear systems subject to time-varying delays, modeled by interval type-2 Takagi–Sugeno fuzzy systems with distinct matrices for each linear subsystem. A non-overestimating adaptation law is introduced to handle matched disturbances with unknown upper bounds, guaranteeing gain convergence once the state trajectory enters a positively invariant practical sliding mode region. The reaching in finite time, the practical sliding mode region, and the practical stability region are all established via upper bounds that do not require any prior knowledge regarding the bound of the disturbance. Delay-dependent sufficient conditions for practical stability under practical sliding mode are derived via a Lyapunov–Krasovskii functional, with explicit dependence on both the delay and the variation rate upper bound of the delay, certifying the uniformly ultimately bounded property of the closed-loop system. The event-triggering mechanism is proven to be Zeno-free. Numerical simulations across three case studies demonstrate the robustness and effectiveness of the proposed strategy, while preserving the practical sliding mode under the most stringent delay conditions.