Dissipativity and Integral Quadratic Constraints, Tailored computational robustness tests for complex interconnections

TL;DR

This paper explores the use of dissipativity and integral quadratic constraints (IQCs) to develop computationally efficient robustness tests for complex feedback interconnections, linking IQC theory with dissipativity for stability analysis.

Contribution

It introduces a unified framework connecting IQCs with dissipativity theory, enhancing the analysis of robust stability and performance in uncertain systems.

Findings

Finite-horizon IQCs with terminal costs bridge IQC theorem and dissipativity.

The approach enables tailored robustness tests for complex interconnections.

The framework simplifies stability analysis via linear matrix inequalities.

Abstract

A central notion in systems theory is dissipativity, which has been introduced by Jan Willems with the explicit goal of arriving at a fundamental understanding of the stability properties of feedback interconnections. In robust control, the framework of integral quadratic constraints (IQCs) builds on the seminal contributions of Yakubovich and Zames in the 1960's. It provides a technique for analyzing the stability of an interconnection of some linear system in feedback with a whole class of systems, also refereed to as uncertainty. In this paper we survey the key ideas of exploiting dissipativity and integral quadratic constraints for the computational analysis of robust stability and performance properties of uncertain interconnections in terms of linear matrix inequalities. In particular for dynamic supply rates, the paper revolves around the notion of finite-horizon integral quadratic constraints with a terminal cost. We reveal that this provides a seamless link between the general IQC theorem and dissipativity theory that has been established only rather recently.