Abstract The study of damping rates for distributed and boundary feedback control systems is important in the design of control mechanisms for distributed parameter systems. Despite the fact that many papers have been published regarding the determination of spectra and also possibly the sharpest systemwide uniform rates of energy decay, many problems remain open. In this paper, we first mention a few examples of distributed and boundary damping, then proceed to examine the simplest such possible case of boundary feedback control of the one-dimensional wave equation. Using the wave propagation method, one can see that the analysis of the spectra is quite sophisticated. Indeed, for most cases, with seemingly the best efforts one can only pin down the rates of damping in some narrow range. Several open questions are posed at the end of the paper, which along with higher dimensional problems we hope will further motivate more studies in such decay spectral analysis.

中文翻译：

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分布参数振动系统阻尼率及边界反馈控制研究

摘要 分布式和边界反馈控制系统阻尼率的研究在分布式参数系统的控制机制设计中具有重要意义。尽管已经发表了许多关于光谱测定以及可能是系统范围内最锐利的均匀能量衰减率的论文，但许多问题仍然悬而未决。在本文中，我们首先提到分布阻尼和边界阻尼的几个例子，然后继续研究一维波动方程的边界反馈控制的最简单的这种可能情况。使用波传播方法，可以看到光谱的分析非常复杂。事实上，在大多数情况下，看似尽了最大努力，也只能将阻尼率确定在某个狭窄的范围内。论文最后提出了几个开放性问题，