Stability radius for infinite-dimensional interconnected systems

TL;DR

This paper investigates the stability radius of infinite-dimensional interconnected systems, providing bounds and formulas under certain conditions, enhancing understanding of system robustness to static perturbations.

Contribution

It introduces new bounds and explicit formulas for the stability radius of interconnected systems with finite-dimensional outputs, extending previous finite-dimensional results to infinite-dimensional settings.

Findings

Lower bound for stability radius based on transfer function norms

Explicit formula for systems with zero feedthrough operator

Applicability to regular linear systems with finite-dimensional outputs

Abstract

The stability radius for finitely many interconnected linear exponentially stable well-posed systems with respect to static perturbations is studied. If the output space of each system is finite-dimensional, then a lower bound for the stability radius in terms of the norm of the corresponding transfer functions is given. Moreover, for regular linear systems with zero feedthrough operator and finite-dimensional output spaces a formula for the stability radius is developed.