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 Neumann'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. (c) 2024 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
