This work studies the problem of exponential stability analysis of the origin of a discrete-time linear system controlled by a ReLU-type Neural Network (NN) that approximates a Model Predictive Control (MPC). Firstly, it is shown that the closed-loop system is equivalent to a Piecewise Affine (PWA) system that can be described by an implicit representation based on ramp functions. Using this representation, conditions in the form of LMIs for the stability certification of the origin of the closed-loop system operated with NN control are derived. In addition, the amplitude constraints on the control signal are taken into account in the stability analysis in the form of a (potentially asymmetric) saturation in the NN output. Finally, a numerical example demonstrates the application of the proposed conditions.