On Problems Involving Eigenvalues for Uncertain Matrices by Structured Singular Values

Abstract

This technical note considers problems that involve eigenvalues of uncertain matrices expressed in linear fractional form using the structured singular value $\mu$ and the skewed structured singular value $\nu$ . In particular, positive definiteness conditions, maximum and minimum eigenvalues, and generalized eigenvalues of uncertain matrices are expressed using $\mu$ and $\nu$ . The obtained results allow us to acquire information of an uncertain matrix efficiently by the existing computational tools that provide practically useful approximations to the values of $\mu$ and $\nu$ .