Nonnegative Matrices and Their Structured Singular Values

Abstract

In this article, we present new results for the computation of structured singular values of nonnegative matrices subject to pure complex perturbations. We prove the equivalence of structured singular values and spectral radius of perturbed matrix \((M\vartriangle )\). The presented new results on the equivalence of structured singular values, nonnegative spectral radius and nonnegative determinant of \((M\vartriangle )\) is presented and analyzed. Furthermore, it has been shown that for a unit spectral radius of \((M\vartriangle )\), both structured singular values and spectral radius are exactly equal. Finally, we present the exact equivalence between structured singular value and the largest singular value of \((M\vartriangle )\).