端口-Hamilton系统指数稳定性的刻画
Characterisation for Exponential Stability of port-Hamiltonian Systems
AI总结：
本文研究能量耗散端口-Hamilton系统的指数能量衰减，利用非自治有限维ODE基本解族的一致有界性给出刻画，并推广已有充分判据、弱化Hamilton密度正则性要求。
摘要：
给定一个能量耗散的端口-Hamilton系统，我们在关于Hamilton密度 $\mathcal{H}$ 的温和条件下，通过模型组成要素刻画能量的指数衰减。顺便，我们通过在很大程度上取消对Hamilton密度的正则性要求，得到了文献中充分判据的推广。使该刻画（以及这些充分判据）成立的关键假设，是某些非自治有限维ODE的一族基本解的一致有界性。先前已知判据中对 $\mathcal{H}$ 的正则性条件（如有界变差）被证明蕴含该关键假设。文中还给出了具有不规则 $L_{\infty}$ 密度的指数稳定端口-Hamilton系统。
英文摘要：
Given an energy-dissipating port-Hamiltonian system, we characterise the exponential decay of the energy via the model ingredients under mild conditions on the Hamiltonian density $\mathcal{H}$. In passing, we obtain generalisations for sufficient criteria in the literature by making regularity requirements for the Hamiltonian density largely obsolete. The key assumption for the characterisation (and thus the sufficient critera) to work is a uniform bound for a family of fundamental solutions for some non-autonomous, finite-dimensional ODEs. Regularity conditions on $\mathcal{H}$ for previously known criteria such as bounded variation are shown to imply the key assumption. Exponentially stable port-Hamiltonian systems with irregular $L_{\infty}$-densities are provided.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
