This paper discusses the stabilizability of artificial neural networks trained by utilizing the gradient information. The method proposed constructs a dynamic model of the conventional update mechanism and derives the stabilizing values of the learning rate. This is achieved by integrating the Error Backpropagation (EBP) technique with Variable Structure Systems (VSS) methodology, which is well known with its robustness to environmental disturbances. In the simulations, control of a three degrees of freedom anthropoid robot is chosen for the evaluation of the performance. For this purpose, a feedforward neural network structure is utilized as the controller. 1 Introduction One of the major problems in the training of Artificial Neural Networks (ANNs) is the lack of stabilizing forces, the existence of which prevents the unbounded growth in the adjustable parameters. Another major problem of the training phase is the robustness, i. e. how well the ANN structure, which is trained on-li..