Dissipativity, Convexity and Tight O'Shea-Zames-Falb Multipliers for Safety Guarantees

TL;DR

This paper introduces a new convex parametrization of integral quadratic constraints using O'Shea-Zames-Falb multipliers, reducing conservatism in stability and optimization analysis, with applications to neural networks and algorithms.

Contribution

It presents a novel convex parametrization framework for integral quadratic constraints involving general multipliers, enhancing analysis precision.

Findings

Reduces conservatism in stability analysis techniques

Provides a new link between convex integrability and dissipativity theory

Sketches applications to neural network stability and optimization algorithms

Abstract

We develop a novel convex parametrization of integral quadratic constraints with a terminal cost for subdifferentials of convex functions, involving general O'Shea-Zames-Falb multipliers. We show the benefit of our results for the reduction of conservatism of existing techniques, and sketch applications to the analysis of optimization algorithms or the stability analysis of neural network controllers. The development is prepared by providing a novel link between the convex integrability of a multivariable mapping and dissipativity theory.