Asymptotic Stability of port-Hamiltonian Systems
Analysis of PDEs
2023-12-12 v2 Mathematical Physics
math.MP
Abstract
We characterise asymptotic stability of port-Hamiltonian systems by means of matrix conditions using well-known resolvent criteria from -semigroup theory. The idea of proof is based on a recent characterisation of exponential stability established in [Trostorff, Waurick, arXiv:2201.10367], which was inspired by a structural observation concerning port-Hamiltonian systems from [Picard et al., arXiv:2106.10937, accepted in SIAM SICON]. We apply the result to study the asymptotic stability of a network of vibrating strings.
Keywords
Cite
@article{arxiv.2210.11775,
title = {Asymptotic Stability of port-Hamiltonian Systems},
author = {Marcus Waurick and Hans Zwart},
journal= {arXiv preprint arXiv:2210.11775},
year = {2023}
}
Comments
20 pages, 1 figure; v2: typos removed, referee's comments incorporated, additional chapters 3 and 5, dealing with exponential stability and applying findings to the vibrating strings example; 29 pages, 1 figure