Approximating the real structured stability radius with Frobenius-norm bounded perturbations

Nicola Guglielmi; Mert Gürbüzbalaban; Tim Mitchell; Michael L. Overton

doi:10.1137/16M1110169

Journal article, 2017

Approximating the real structured stability radius with Frobenius-norm bounded perturbations

Nicola Guglielmi, Mert Gürbüzbalaban, Tim Mitchell, Michael L. Overton

SIAM Journal on Matrix Analysis and Applications, 38(4), pp. 1323–1353, 2017.

Publisher (DOI)

In brief

The real structured stability radius measures how large a real, structured perturbation a dynamical system can tolerate before losing stability. The paper shows the worst perturbations in the Frobenius norm can be taken to have rank at most two and builds an iterative method around that fact, which approximates the radius efficiently where the general problem is intractable.

Topics

Spectral & nonsmooth optimization

Cite

@article{guglielmi2017radius,
  title   = {Approximating the real structured stability radius with Frobenius-norm bounded perturbations},
  author  = {Nicola Guglielmi and Mert Gürbüzbalaban and Tim Mitchell and Michael L. Overton},
  year    = {2017},
  journal = {SIAM Journal on Matrix Analysis and Applications},
  volume  = {38(4)},
  pages   = {1323--1353},
  doi     = {10.1137/16M1110169},
}