Bounding Stability Constants for Affinely Parameter-Dependent Operators

TL;DR

This paper presents a novel approach to bounding stability constants for affinely parameter-dependent operators, enabling offline guarantees of stability and extending to Lyapunov stability in dynamical systems.

Contribution

It introduces a new framework for bounding stability constants over neighborhoods, improving stability guarantees in reduced basis methods and dynamical systems.

Findings

Bounding stability constants over neighborhoods is feasible.

Stability guarantees can be obtained offline.

Lyapunov stability analysis is incorporated into the framework.

Abstract

In this article we introduce new possibilities of bounding the stability constants that play a vital role in the reduced basis method. By bounding stability constants over a neighborhood we make it possible to guarantee stability at more than a finite number of points and to do that in the offline stage. We additionally show that Lyapunov stability of dynamical systems can be handled in the same framework.