Stable-by-Design Neural Network-Based LPV State-Space Models for System Identification

Accurate modeling of nonlinear systems is essential for reliable control, yet conventional identification methods often struggle to capture latent dynamics while maintaining stability. We propose a $\mathit{\text{stable-by-design}}\mathit{\text{LPV}}\mathit{\text{neural}}\mathit{\text{network-based}}\mathit{\text{state-space}}$ (NN-SS) model that simultaneously learns latent states and internal scheduling variables directly from data. The state-transition matrix, generated by a neural network using the learned scheduling variables, is guaranteed to be stable through a Schur-based parameterization. The architecture combines an encoder for initial state estimation with a state-space representer network that constructs the full set of scheduling-dependent system matrices. For training the NN-SS, we develop a framework that integrates multi-step prediction losses with a state-consistency regularization term, ensuring robustness against drift and improving long-horizon prediction accuracy. The proposed NN-SS is evaluated on benchmark nonlinear systems, and the results demonstrate that the model consistently matches or surpasses classical subspace identification methods and recent gradient-based approaches. These findings highlight the potential of stability-constrained neural LPV identification as a scalable and reliable framework for modeling complex nonlinear systems.