This article studies the fault‐tolerant control for linear systems with disturbances through sliding mode scheme. Compared with the existing results, by means of a nonlinear sliding function with an exponential term, a reduced‐order sliding motion can be obtained while the reaching phase of conventional sliding mode control is eliminated. On the other side, with the help of an exponentially decaying barrier Lyapunov functions, a continuous sliding mode algorithm is established. Within the proposed framework, the trajectories of closed‐loop systems can be forced to a prescribed practical sliding surface, and then, both the transient as well as steady‐state performances are guaranteed despite the occurrence of abrupt actuator faults. Under the Lyapunov direct method, a sufficient condition is derived such that the sliding motion is uniformly bounded with time‐varying performance constraints. Finally, an electric amplidyne system is considered to demonstrate the theoretical results.

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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.

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