Data-driven Stability Analysis of Neural Network Control Systems

This letter studies the problem of verifying stability of neural network control systems in which the plant dynamics are unknown but the neural network controller is known. We derive sufficient conditions for stability that are directly computable from a finite-length trajectory of the closed-loop system, without requiring an explicit model of the plant. The proposed conditions take the form of linear matrix inequalities and, as a byproduct, yield an estimate of the region of attraction. Both the noiseless and noisy data settings are considered: in the noiseless case, data-driven sufficient conditions are derived to guarantee stability; in the noisy case, sufficient conditions are derived to ensure robust stability of all systems consistent with the data. The effectiveness of the proposed approach is demonstrated on an inverted pendulum example.