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Both state and output feedback adaptive neural network controls are developed for a class of discrete-time single-input single-output (SISO) nonaffine uncertain nonlinear systems. Each controller incorporates a linear dynamic compensator and an adaptive neural network term. The linear dynamic compensator is designed to stabilize the linearized system, and the adaptive neural network term is introduced to deal with nonlinearity. The closed-loop systems are proved to be semi-globally uniformly ultimately bounded (SGUUB) by using linear matrix inequality (LMI). Simulation of a liquid level system illustrates the effectiveness of proposed controls.