论文标题
采样数据的强稳定性
Strong Stability of Sampled-data Riesz-spectral Systems
论文作者
论文摘要
假设具有静态反馈控制器的连续时间线性无限维系统非常稳定。我们解决了以下问题：如果我们通过应用理想的采样器和零订单保持，将连续时间控制器转换为采样数据控制器，那么所得的采样数据系统是否在所有足够小的采样期内都能稳定？在本文中，我们将注意力限制在开环系统的发电机是Riesz-Spectral运算符的情况下，其点频谱在原点上具有一个极限点。我们提出了上述问题的答案是肯定的条件。在鲁棒性分析中，我们表明，在快速采样下，在原始连续时系统和采样数据系统之间保留了在Arendt-Batty-Lyubich-Vũ定理中获得的足够稳定性条件。
Suppose that a continuous-time linear infinite-dimensional system with a static state-feedback controller is strongly stable. We address the following question: If we convert the continuous-time controller to a sampled-data controller by applying an idealized sampler and a zero-order hold, will the resulting sampled-data system be strongly stable for all sufficiently small sampling periods? In this paper, we restrict our attention to the situation where the generator of the open-loop system is a Riesz-spectral operator and its point spectrum has a limit point at the origin. We present conditions under which the answer to the above question is affirmative. In the robustness analysis, we show that the sufficient condition for strong stability obtained in the Arendt-Batty-Lyubich-Vũ theorem is preserved between the original continuous-time system and the sampled-data system under fast sampling.
