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In this paper, the problem of robust output tracking control for a class of time-delay nonlinear systems is considered. The systems are in the form of triangular structure with unmodeled dynamics. First, we construct an observer whose gain matrix is scheduled via linear matrix inequality approach. For the case that the information of uncertainties bounds is not completely available, we design an observer-based neural network (NN) controller by employing the backstepping method. The resulting closed-loop system is ensured to be stable in the sense of semiglobal boundedness with the help of changing supplying function idea. The observer and the controller designed are both independent of the time delays. Finally, numerical simulations are conducted to verify the effectiveness of the main theoretic results obtained.