Positive trigonometric polynomials for strong stability of difference equations
Optimization and Control
2010-11-08 v1
Abstract
We follow a polynomial approach to analyse strong stability of linear difference equations with rationally independent delays. Upon application of the Hermite stability criterion on the discrete-time homogeneous characteristic polynomial, assessing strong stability amounts to deciding positive definiteness of a multivariate trigonometric polynomial matrix. This latter problem is addressed with a converging hierarchy of linear matrix inequalities (LMIs). Numerical experiments indicate that certificates of strong stability can be obtained at a reasonable computational cost for state dimension and number of delays not exceeding 4 or 5.
Cite
@article{arxiv.1011.1331,
title = {Positive trigonometric polynomials for strong stability of difference equations},
author = {Didier Henrion and Tomas Vyhlidal},
journal= {arXiv preprint arXiv:1011.1331},
year = {2010}
}