端口哈密顿系统的渐近稳定性
偏微分方程分析
2023-12-12 v2 数学物理
math.MP
摘要
我们利用 -半群理论中著名的预解判据,通过矩阵条件刻画端口哈密顿系统的渐近稳定性。证明思想基于 [Trostorff, Waurick, arXiv:2201.10367] 中建立的指数稳定性近期刻画,其受 [Picard et al., arXiv:2106.10937, accepted in SIAM SICON] 中关于端口哈密顿系统的结构观察启发。我们将该结果应用于研究振动弦网络的渐近稳定性。
引用
@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}
}
备注
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