An Overview of Integral Quadratic Constraints for Delayed Nonlinear and Parameter-Varying Systems

TL;DR

This paper introduces a unified framework using integral quadratic constraints (IQCs) to analyze the stability and performance of nonlinear and parameter-varying systems with delays, providing new IQCs and demonstrating their effectiveness through numerical examples.

Contribution

It develops new IQCs for constant and varying delays and integrates them into dissipation inequalities for stability and performance analysis of delayed systems.

Findings

New IQCs for constant and varying delays

Effective bounds on system performance using IQCs

Numerical examples validate the proposed framework

Abstract

A general framework is presented for analyzing the stability and performance of nonlinear and linear parameter varying (LPV) time delayed systems. First, the input/output behavior of the time delay operator is bounded in the frequency domain by integral quadratic constraints (IQCs). A constant delay is a linear, time-invariant system and this leads to a simple, intuitive interpretation for these frequency domain constraints. This simple interpretation is used to derive new IQCs for both constant and varying delays. Second, the performance of nonlinear and LPV delayed systems is bounded using dissipation inequalities that incorporate IQCs. This step makes use of recent results that show, under mild technical conditions, that an IQC has an equivalent representation as a finite-horizon time-domain constraint. Numerical examples are provided to demonstrate the effectiveness of the method for both class of systems.