Sliding mode control for non‐linear systems by Takagi–Sugeno fuzzy model and delta operator approaches

This study considers the problem of adaptive sliding mode control for discrete‐time Takagi–Sugeno (T–S) fuzzy systems with actuator faults and external disturbances via the delta operator method. The delta operator approach is used to represent the discrete‐time non‐linear systems described by T–S fuzzy models. The actuator fault considered in this study is unknown and its fault‐deviation is also unknown. A reduced‐order system is utilised to design the sliding mode surface subject to linear matrix inequality constraint. By constructing the sliding mode surface, a novel adaptive sliding mode controller is designed to guarantee that the closed‐loop system is uniformly ultimately bounded. Finally, two practical examples are presented to show the effectiveness and applicability of the developed fault‐tolerant control scheme.