论文标题
港口港口系统的指数稳定性表征
Characterisation for Exponential Stability of port-Hamiltonian Systems
论文作者
论文摘要
鉴于驱散港口港口系统的能量，我们在轻度条件下通过模型成分在汉密尔顿密度$ \ mathcal {h} $上通过模型成分来表征能量的指数衰减。顺便说一句，我们通过对哈密顿密度的规律性要求在很大程度上过时获得了文献中足够的标准的概括。对表征（以及足够的标准）工作的关键假设是用于某些非自治，有限维的ODE的基本解决方案家族的统一假设。对于先前已知的标准（例如有限变化），$ \ Mathcal {H} $上的规律性条件被证明暗示着关键假设。具有不规则的$ l _ {\ infty} $的指数稳定的港口 - 哈米尔顿港系统 - 提供了密度。
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.
