The paper describes an algorithm for the synthesis of neural networks to control gyro stabilizer. The neural network performs the role of observer for state vector. The role of an observer in a feedback of gyro stabilizer is illustrated. Paper detail a problem specific features stage of classics algorithm: choosing of network architecture, learning of neural network and verification of result feedback control. In the article presented optimal configuration of the neural network like a memory depth, the number of layers and neuron in these layers and activation functions in layers. Using the information of dynamic system for improving learning of neural network is provided. A scheme creation of an optimal training sample is provided.