  This paper proposes a data-driven approach to design a feedforward Neural
Network (NN) controller with a stability guarantee for systems with unknown
dynamics. We first introduce data-driven representations of stability
conditions for Neural Feedback Loops (NFLs) with linear plants. These
conditions are then formulated into a semidefinite program (SDP). Subsequently,
this SDP constraint is integrated into the NN training process resulting in a
stable NN controller. We propose an iterative algorithm to solve this problem
efficiently. Finally, we illustrate the effectiveness of the proposed method
and its superiority compared to model-based methods via numerical examples.
