On stabilizability and sampling for infinite dimensional systems
On stabilizability and sampling for infinite dimensional systems
复制标题
无限维系统的稳定性和采样
DOI：
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发表时间：
1992
期刊：
影响因子：
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通讯作者：
C. Wang
中科院分区：
文献类型：
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作者：
I. Rosen;C. Wang
考虑了一些关于无限维或分布参数系统的稳定性的问题，这些问题要么是由时间采样引发的，要么是与时间采样相关的。特别是，这些包括有限秩可稳定的系统的特征，以及在采样下保持稳定性。识别出一类病态的系统，在采样时，该系统可能会因采样率中的任意小扰动而变得不稳定。建立这些结果所采用的方法基于基础开环半群的无穷小生成元的谱分解。获得的结果适用于具有由应用中经常出现的广泛类别的偏微分方程和函数微分方程描述的动力学的控制系统。 >
Some questions, either motivated by or related to time sampling, regarding the stabilizability of infinite-dimensional or distributed parameter systems are considered. In particular, these include the characteristics of those systems which are finite rank stabilizable, and the preservation of stabilizability under sampling. A pathological class of systems, which, when sampled, may be rendered unstabilizable by arbitrarily small perturbations in the sampling rate, is identified. The approach taken in establishing these results is based upon a spectral decomposition of the infinitesimal generator of the underlying open-loop semigroup. The results obtained apply to control systems with dynamics described by broad classes of partial and functional differential equations that arise frequently in applications. >