We prove that every semidefinite moment relaxation of a polynomial optimization problem
(POP) with a ball constraint can be reformulated as a semidefinite program involving a …

This paper is concerned with the computation of the local Lipschitz constant of feedforward
neural networks (FNNs) with activation functions being rectified linear units (ReLUs). The …

This paper is concerned with the stability analysis of the recurrent neural networks (RNNs)
by means of the integral quadratic constraint (IQC) framework. The rectified linear unit …

This paper presents sufficient conditions for the stability and $\ell_2 $-gain performance of
recurrent neural networks (RNNs) with ReLU activation functions. These conditions are …

In this work we propose a new data-based approach for robust controller design for a rather
general class of recurrent neural networks affected by bounded measurement noise. We first …

Abstract Machine learning tools are widely used for knowledge extraction, modeling, and
decision tasks; a range of problems that Control Theory also tackles. Their relations have …

This paper is concerned with the analysis of the $ L_p\(p\in [1,\infty), p=\infty) $ induced
norms of continuous-time linear systems where input signals are restricted to be …

This paper is concerned with the stability/instability analysis problem of feedback systems
with rectified linear unit (ReLU) nonlinearities. Such feedback systems arise when we model …

This paper derives a complete set of quadratic constraints (QCs) for the repeated ReLU. The
complete set of QCs is described by a collection of matrix copositivity conditions. We also …

This paper is concerned with the stability analysis problem of feedback systems with rectified
linear unit (ReLU) nonlinearities. Such feedback systems arise when we model dynamical …