Computing the nearest stable matrix pairs

Authors

Nicolas Gillis, Volker Mehrmann, Punit Sharma

Abstract

In this paper, we study the nearest stable matrix pair problem: given a square matrix pair (E,A), minimize the Frobenius norm of (ΔE,ΔA) such that (E+ΔE,A+ΔA) is a stable matrix pair. We propose a reformulation of the problem with a simpler feasible set by introducing dissipative Hamiltonian matrix pairs: A matrix pair (E,A) is dissipative Hamiltonian if A=(J−R)Q with skew‐symmetric J, positive semidefinite R, and an invertible Q such that QTE is positive semidefinite. This reformulation has a convex feasible domain onto which it is easy to project. This allows us to employ a fast gradient method to obtain a nearby stable approximation of a given matrix pair.

Citation

• Journal: Numerical Linear Algebra with Applications
• Year: 2018
• Volume: 25
• Issue: 5
• Pages:
• Publisher: Wiley
• DOI: 10.1002/nla.2153

BibTeX

@article{Gillis_2018,
  title={{Computing the nearest stable matrix pairs}},
  volume={25},
  ISSN={1099-1506},
  DOI={10.1002/nla.2153},
  number={5},
  journal={Numerical Linear Algebra with Applications},
  publisher={Wiley},
  author={Gillis, Nicolas and Mehrmann, Volker and Sharma, Punit},
  year={2018}
}

Download the bib file

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