A novel method to approximate structured stability radii
Nicola Guglielmi, Manuela Manetta · AIP conference proceedings · 2013
The unstructured stability radius of a Hurwitz matrix A (i.e. a matrix whose eigenvalues have strictly negative real part) is the smallest norm of a complex perturbation E such that A + E is not Hurwitz, which means it has at least an eigenvalue with zero real part. Such a measure is a more robust stability indicator with respect to the spectral abscissa and is much studied in the literature. However, when the matrix A has a structure (for example the matrix is real or has a prescribed sparsity pattern), it would be more meaningful to look for the smallest destabilizing perturbation E with the same structure. This problem turns out to be more difficult and in some cases unresolved. We propose here a new methodology to compute approximations of the structured stability radii, focusing our attention on real and pattern-structured stability radii.