  In this work, we propose a dissipativity-based method for Lipschitz constant
estimation of 1D convolutional neural networks (CNNs). In particular, we
analyze the dissipativity properties of convolutional, pooling, and fully
connected layers making use of incremental quadratic constraints for nonlinear
activation functions and pooling operations. The Lipschitz constant of the
concatenation of these mappings is then estimated by solving a semidefinite
program which we derive from dissipativity theory. To make our method as
efficient as possible, we exploit the structure of convolutional layers by
realizing these finite impulse response filters as causal dynamical systems in
state space and carrying out the dissipativity analysis for the state space
realizations. The examples we provide show that our Lipschitz bounds are
advantageous in terms of accuracy and scalability.
