Exact Solution for the Rank-One Structured Singular Value with Repeated Complex Full-Block Uncertainty
Abstract
In this note, we present an exact solution for the structured singular value (SSV) of rank-one complex matrices with repeated complex full-block uncertainty. A key step in the proof is the use of Von Neumman's trace inequality. Previous works provided exact solutions for rank-one SSV when the uncertainty contains repeated (real or complex) scalars and/or non-repeated complex full-block uncertainties. Our result with repeated complex full-blocks contains, as special cases, the previous results for repeated complex scalars and/or non-repeated complex full-block uncertainties. The repeated complex full-block uncertainty has recently gained attention in the context of incompressible fluid flows. Specifically, it has been used to analyze the effect of the convective nonlinearity in the incompressible Navier-Stokes equation (NSE). SSV analysis with repeated full-block uncertainty has led to an improved understanding of the underlying flow physics. We demonstrate our method on a turbulent channel flow model as an example.
Cite
@article{arxiv.2307.02069,
title = {Exact Solution for the Rank-One Structured Singular Value with Repeated Complex Full-Block Uncertainty},
author = {Talha Mushtaq and Peter Seiler and Maziar S. Hemati},
journal= {arXiv preprint arXiv:2307.02069},
year = {2023}
}