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.