Adaptive Sliding Mode Control Design for Interval Type‐2 T–S Fuzzy Systems With Time Delay: An Event‐Triggered Approach

ABSTRACT In this work, a new event‐triggered adaptive first‐order sliding mode control method is proposed for nonlinear systems with constant time delays, modeled by interval type‐2 Takagi–Sugeno (T–S) fuzzy systems. To handle matched disturbances with unknown upper bounds, a non‐overestimating adaptation strategy for the control coefficient is developed. Finite‐time convergence to the practical sliding mode region between events is guaranteed, with a convergence time upper bound that is independent of the prior knowledge of the matched disturbance upper bound. The practical stability analysis is established under delay‐dependent sufficient conditions. It is demonstrated that the practical sliding mode region is a positively invariant set, defined without requiring prior knowledge of the matched disturbance upper bound. The proposed method establishes a certification for the Uniform Ultimately Bounded (UUB) property through exponential decay, showing that the decay rate directly influences the tightness of the practical stability region. Furthermore, the sequence of event‐triggering instants is guaranteed to be Zeno‐free. Computational simulations conducted via three case studies demonstrate the effectiveness of the proposed control strategy.