A Right Coprime Factorization of Neural State Space Models

In recent years, various methods for identification of nonlinear systems in closed loop using open-loop approaches have received considerable attention. However, these methods rely on differentially coprime factorizations of the nonlinear plants, which can be difficult to compute in practice. To address this issue, this paper presents various technical results leading up to explicit formulae for right coprime factorizations of neural state space models, i.e., nonlinear system models represented in state space using neural networks, which satisfy a Bezout identity.