The advantage of neural network controllers to address robot trajectory tracking errors due to dynamic parameter uncertainties has been widely recognized. Despite many publications in the field of neural networks applied to repetitive robotic task execution, the lack of quantitative performance analysis impedes the application of neural networks in industry. The objective of this thesis is to formulate a systematic approach to analyze the mathematical relation between the performance and parameters of the neural network control robot system, i.e., the sensitivity of the system performance to parameters. This provides a better understanding how the neural network controller performs after the neural network is trained, a condition in which robot systems typically operate. First, the complete dynamic system is treated as a two-time-scale dynamics system, based on the perturbation theory. The learning rate is considered as a small parameter, the robot and neural network dynamics are regarded as fast and slow dynamic systems respectively. Then, the solution bound approach is employed to bound the norm of the system solutions. Finally, the influence of the system parameters, such as the robot payload and link mass etc., on the system performance, measured by the system error norm, is investigated using sensitivity analysis. Experimental results obtained with an industrial robot demonstrate the validity of the proposed approach. Above all, the quantification of the performance issue provides further justification for the commercialization of neural networks to robot systems. The future impact of this thesis is that it gives the basis to formulate an approach for synthesis of neural network control systems with guaranteed performance.