On approximating the nearest \Omega-stable matrix
Abstract
In this paper, we consider the problem of approximating a given matrix with a matrix whose eigenvalues lie in some specific region \Omega, within the complex plane. More precisely, we consider three types of regions and their intersections: conic sectors, vertical strips and disks. We refer to this problem as the nearest \Omega-stable matrix problem. This includes as special cases the stable matrices for continuous and discrete time linear time-invariant systems. In order to achieve this goal, we parametrize this problem using dissipative Hamiltonian matrices and linear matrix inequalities. This leads to a reformulation of the problem with a convex feasible set. By applying a block coordinate descent method on this reformulation, we are able to compute solutions to the approximation problem, which is illustrated on some examples.
Keywords
Cite
@article{arxiv.1901.03069,
title = {On approximating the nearest \Omega-stable matrix},
author = {Neelam Choudhary and Nicolas Gillis and Punit Sharma},
journal= {arXiv preprint arXiv:1901.03069},
year = {2024}
}
Comments
14 pages, 3 figures