Membership functions dependent adaptive sliding mode fault‐tolerant control for uncertain T–S fuzzy systems with performance bounds

Summary This article is concerned with the problem of adaptive sliding mode control for uncertain Takagi–Sugeno fuzzy systems in the presence of actuator faults. In order to accommodate fuzzy systems, a membership function weights dependent sliding function is first given. Compared with the existing linear sliding function based results, a reduced‐order fuzzy sliding motion through parallel distributed compensation structure is obtained, then less conservative results are achieved. By exploiting a restricted potential function, a continuous sliding mode fault‐tolerant control scheme is established. Then the closed‐loop system trajectory is maintained in practical sliding mode with a preset sliding band, which improves the robustness performances of system especially for the occurrence of abrupt actuator faults. Moreover, with the usage of the property of fuzzy product inference engines through equivalence class in set theory, a less conservative stability criterion in terms of linear matrix inequalities is derived to guarantee the uniformly boundedness of the reduced‐order sliding motion. At last, some illustrative examples are offered to validate the effectiveness of our proposal.