Exponential Convergence Bounds using Integral Quadratic Constraints

TL;DR

This paper introduces a modified IQC framework that provides a practical computational method for certifying exponential convergence rates in systems with nonlinearities or uncertainties.

Contribution

It presents a novel modification of classical IQC results enabling efficient computation of exponential decay rate bounds.

Findings

Provides a tractable method for exponential rate certification.

Enhances the applicability of IQCs to stability analysis.

Offers numerical tools for system stability guarantees.

Abstract

The theory of integral quadratic constraints (IQCs) allows verification of stability and gain-bound properties of systems containing nonlinear or uncertain elements. Gain bounds often imply exponential stability, but it can be challenging to compute useful numerical bounds on the exponential decay rate. In this work, we present a modification of the classical IQC results of Megretski and Rantzer that leads to a tractable computational procedure for finding exponential rate certificates.