$\nu$-Analysis: A New Notion of Robustness for Large Systems with Structured Uncertainties

TL;DR

This paper introduces a scalable robustness measure called $ u$ for large systems with structured uncertainties, offering a convex upper bound and new theoretical insights, improving robustness analysis beyond traditional methods.

Contribution

The paper proposes a novel robustness measure $ u$, providing a convex upper bound and establishing a relationship with non-negative matrices, advancing large-scale robust control analysis.

Findings

$ u$ offers a scalable alternative to structured singular value.

The measure provides a convex upper bound for robustness analysis.

Theoretical link between robust control and non-negative matrices is established.

Abstract

We present a new, scalable alternative to the structured singular value, which we call $\nu$, provide a convex upper bound, study their properties and compare them to $\ell_1$ robust control. The analysis relies on a novel result on the relationship between robust control of dynamical systems and non-negative constant matrices.