A Novel hybrid backstepping interval type-2fuzzy adaptive control (HBT2AC) for uncertain discrete-time nonlinear systems is presented in this paper. The systems are assumed to be defined with the aid of discrete equations with nonlinear uncertainties which are considered as modeling errors and external unknown disturbances, and that the observed states are considered disturbed. The adaptive fuzzy type-2 controller is designed, where the fuzzy inference approach based on extended single-input rule modules (SIRMs) approximate the modeling errors, non-measurable states and adjustable parameters are estimated using derived weighted simplified least squares estimators (WSLS). We can prove that the states are bounded and the estimation errors stand in the neighborhood of zero. The efficiency of the approach is proved by simulation for which the root mean squares criteria are used which improves control performance.

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