You can mathematically guarantee that recurrent neural networks and control systems remain stable by checking specific matrix conditions, enabling you to design more reliable AI systems with fewer parameters.
This paper develops mathematical tools for designing stable neural networks and control systems. It introduces a 'nonlinear separation principle' that guarantees stability when combining controllers and observers, derives conditions for ensuring neural networks behave predictably, and shows how to use these insights to build efficient deep learning models that maintain stability while learning.