2023/07/05 by Talha Mushtaq, Peter Seiler, Mushtaq, Talha +3 · 1 citation
Decision Sciences · Mathematics · #FOS: Electrical engineering #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Optimization and Control (math.OC) #Probabilistic and Robust Engineering Design #Statistical and numerical algorithms #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2307.02069
openalex publication_date 2023/07/05 · openalex created_date 2023/07/07 · openalex updated_date 2026/08/01
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.