A new adaptive neural network (NN) output-feedback stabilization controller is investigated for a class of uncertain stochastic nonlinear strict-feedback systems with discrete and distributed time-varying delays and unknown nonlinear functions in both drift and diffusion terms. First, an extensional stability notion and the related criterion are introduced. Then, a nonlinear observer to estimate the unmeasurable states is designed, and a systematic backstepping procedure to design an adaptive NN output-feedback controller is proposed such that the closed-loop system is stable in probability. The effectiveness of the proposed control scheme is demonstrated via a numerical example.

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