On realizability of neural networks-based input–output models in the classical state-space form

This paper proves that the typical neural network-based input/output model does not have a state-space realization and suggests the Additive Nonlinear Auto-Regressive with eXogenous input (ANARX) structure as an excellent choice for neural-network-based input–output models. The advantage of the ANARX model is that the time-steps in the argument are pair-wise decomposed, which allows the ANARX model to be realized in state space, and to be linearized via dynamic output feedback. Moreover, accessibility of the state-space realization has been proved.