This work proposes a new learning strategy for training a feedforward neural network subject to spectral norm and nonnegativity constraints. Our primary goal is to control the Lipschitz constant of the network in order to make it robust against adversarial perturbations of its inputs. We propose a stochastic projected gradient descent algorithm which allows us to adjust this constant in the training process. The algorithm is evaluated in the context of designing a fully connected network for Automatic Gesture Recognition based on EMG signals. We perform a comparison with the same architecture trained either in a standard manner or with simpler constraints. The obtained results highlight that a good accuracy-robustness trade-off can be achieved