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This paper studies the problem of robust sliding mode control (SMC) for a class of nonlinear systems subject to actuator failures and disturbances. By employing a novel integral sliding function constructed with an nested sliding mode controller "ν(t)$$ \nu (t) $$," a dual‐layer sliding mode control is established. The first layer is an integral sliding mode generated by the actuator output, the second one is a linear sliding mode generated by "ν(t)$$ \nu (t) $$." Indeed, the linear sliding mode is nested to the integral sliding mode for the system under consideration. Compared with the state‐of‐the‐art integral sliding mode controls (ISMCs), not only the inherent robustness of ISMC is retained, but also the time derivative of integral sliding function in integral sliding motion dynamics can be compensated by "ν(t)$$ \nu (t) $$," so that the robustness of integral sliding motion is further enhanced. Furthermore, due to the generation of the nested linear sliding mode, it decouples the matched integral sliding function time derivative of integral sliding motion dynamics from the mismatched disturbance. This decoupling facilitates the design of "ν(t)$$ \nu (t) $$" through ℋ∞$$ {\mathscr{H}}_{\infty } $$ control theory, then, the closed‐loop systems are ensured to be asymptotically stable with ℋ∞$$ {\mathscr{H}}_{\infty } $$ performance. Lastly, with two classes of barrier functions exploited for the design of sliding mode controllers, both sliding modes cannot be lost for system responses even in the presence of unforeseen actuator failures and disturbances. In simulation, an IEEE 6 bus power system is offered to demonstrate the superiorities of the theoretical results. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]