# Computing nearest stable matrix pairs

arXiv: https://arxiv.org/abs/1704.03184 · HTML: https://mlsanity.com/paper/1704.03184/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2017.

## Built on by (most cited first, 1 of 1)

- [Data-driven identification of latent port-Hamiltonian systems](https://mlsanity.com/paper/2408.08185/) (2024)

## Abstract (arXiv)

In this paper, we study the nearest stable matrix pair problem: given a square matrix pair (E,A), minimize the Frobenius norm of (DeltaE,DeltaA) such that (E+DeltaE,A+DeltaA) is a stable matrix pair. We propose a reformulation of the problem with a simpler feasible set by introducing dissipative Hamiltonian (DH) matrix pairs: A matrix pair (E,A) is DH 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.