Gillis, NicolasMehrmann, VolkerSharma, Punit2021-12-172021-12-172017-04-122197-8085https://depositonce.tu-berlin.de/handle/11303/15895http://dx.doi.org/10.14279/depositonce-14668In this paper, we study the nearest stable matrix pair problem: given a square matrix pair (E,A), minimize the Frobenius norm of (∆E,∆A) such that (E+\∆E,A+∆A) is a stable matrix pair. We propose a reformulation of the problem with a simpler feasible set byintroducing 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 Q^TE 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.en510 Mathematikdissipative Hamiltonian systemdistance to stabilityconvex optimizationResearch Paper