Approximation performance analysis of recurrent neural networks

On the basis of the transformation from the space state model into the input/output model for the general recurrent neural networks, we prove that recurrent networks may realize entire approximation to arbitrary non-linear property under some conditions. And point out that in order to realize arbitrary non-linear function approximation using recurrent neural networks, the initial conditions, the number of node in hidden layer and the approximation effectiveness must be considered. The complete network design process is given through the numerical example to verify the results obtained.