Integral Quadratic Constraints on Linear Infinite-dimensional Systems for Robust Stability Analysis
Optimization and Control
2026-03-03 v2 Analysis of PDEs
Abstract
This paper proposes a framework to assess the stability of an ordinary differential equation which is coupled to a 1D-partial differential equation (PDE). The stability theorem is based on a new result on Integral Quadratic Constraints (IQCs) and expressed in terms of two linear matrix inequalities with a moderate computational burden. The IQCs are not generated using dissipation inequalities involving the whole state of an infinite-dimensional system, but by using projection coefficients of the infinite-dimensional state. This permits to generalize our robustness result to many other PDEs. The proposed methodology is applied to a time-delay system and numerical results comparable to those in the literature are obtained.
Cite
@article{arxiv.2003.06283,
title = {Integral Quadratic Constraints on Linear Infinite-dimensional Systems for Robust Stability Analysis},
author = {Matthieu Barreau and Carsten W. Scherer and Frederic Gouaisbaut and Alexandre Seuret},
journal= {arXiv preprint arXiv:2003.06283},
year = {2026}
}