Stability Properties of Minimal Gated Unit Neural Networks

Recurrent neural networks, such as Gated Recurrent Unit (GRU) networks, are widely adopted in system identification due to their ability to model nonlinear dynamical behaviors. However, their complexity poses barriers for embedded applications requiring low memory footprint and fast inference. Furthermore, standard training does not guarantee Input-to-State Stability (ISS) or Incremental ISS (δISS). These properties are vital not only for safe control deployment [3], but also to ensure that the identified model is physically consistent, preventing unbounded predictions in long-term simulations. In this work, we analyze Minimal Gated Unit (MGU) networks [1], lightweight architectures simplifying GRU networks. We extend the stability analysis framework from [3] to the MGU network, deriving sufficient parametric conditions for δISS, and propose a stability-promoting training strategy. Validation shows this yields safe models without sacrificing accuracy