Conal Distances Between Rational Spectral Densities
Optimization and Control
2018-02-20 v2
Abstract
The paper generalizes Thompson and Hilbert metric to the space of spectral densities. The resulting complete metric space has the differentiable structure of a Finsler manifold with explicit geodesics. The resulting distances are filtering invariant, can be computed efficiently, and admit geodesic paths that preserve rationality; these are properties of fundamental importance in many engineering applications.
Cite
@article{arxiv.1708.02818,
title = {Conal Distances Between Rational Spectral Densities},
author = {Giacomo Baggio and Augusto Ferrante and Rodolphe Sepulchre},
journal= {arXiv preprint arXiv:1708.02818},
year = {2018}
}
Comments
24 pages, 4 figures. Revised version: title has been changed, several parts have been rewritten, two sections have been added (one illustrating some motivating examples, the other concerning a numerical example). Submitted for publication