  Adversarial examples can easily degrade the classification performance in
neural networks. Empirical methods for promoting robustness to such examples
have been proposed, but often lack both analytical insights and formal
guarantees. Recently, some robustness certificates have appeared in the
literature based on system theoretic notions. This work proposes an incremental
dissipativity-based robustness certificate for neural networks in the form of a
linear matrix inequality for each layer. We also propose an equivalent spectral
norm bound for this certificate which is scalable to neural networks with
multiple layers. We demonstrate the improved performance against adversarial
attacks on a feed-forward neural network trained on MNIST and an Alexnet
trained using CIFAR-10.
