Differentially positive systems
Systems and Control
2014-11-12 v2 Dynamical Systems
Abstract
The paper introduces and studies differentially positive systems, that is, systems whose linearization along an arbitrary trajectory is positive. A generalization of Perron Frobenius theory is developed in this differential framework to show that the property induces a (conal) order that strongly constrains the asymptotic behavior of solutions. The results illustrate that behaviors constrained by local order properties extend beyond the well-studied class of linear positive systems and monotone systems, which both require a constant cone field and a linear state space.
Cite
@article{arxiv.1405.6298,
title = {Differentially positive systems},
author = {Fulvio Forni and Rodolphe Sepulchre},
journal= {arXiv preprint arXiv:1405.6298},
year = {2014}
}
Comments
32 pages, 10 figures