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In this paper, an adaptive fuzzy hierarchical sliding-mode control method for a class of multiinput multioutput unknown nonlinear time-delay systems with input saturation is proposed. The studied system is first transformed into an equivalent system. Subsequently, based on sliding-mode control technology and the concept of hierarchical design, a set of adaptive fuzzy hierarchical sliding-mode controllers are designed for the new defined system by using fuzzy systems to approximate uncertain functions and compensate input saturation. Choosing an appropriate Lyapunov-Krasovskii function, it is theoretically proved that all the signals in the closed-loop system together with the proposed sliding surfaces are uniformly ultimately bounded under our designed adaptive fuzzy controllers. Simulation results demonstrate the effectiveness of the proposed design techniques for the systems under consideration.
Zhao et al. (Wed,) studied this question.