Stability analysis by dynamic dissipation inequalities: On merging frequency-domain techniques with time-domain conditions

TL;DR

This paper introduces a novel stability analysis method that combines dissipation theory with frequency-domain techniques, enabling transient response constraints and robust ellipsoid generation for feedback systems.

Contribution

It provides a new stability characterization linking dissipation theory and integral quadratic constraints, facilitating transient response guarantees and robust ellipsoid computation.

Findings

Established a complete link between dissipation theory and IQC-based stability analysis.

Developed a method for guaranteeing transient response constraints in feedback systems.

Demonstrated the approach with a numerical example on parametric robustness.

Abstract

In this paper we provide a complete link between dissipation theory and a celebrated result on stability analysis with integral quadratic constraints. This is achieved with a new stability characterization for feedback interconnections based on the notion of finite-horizon integral quadratic constraints with a terminal cost. As the main benefit, this opens up opportunities for guaranteeing constraints on the transient responses of trajectories in feedback loops within absolute stability theory. For parametric robustness, we show how to generate tight robustly invariant ellipsoids on the basis of a classical frequency-domain stability test, with illustrations by a numerical example.