We introduce a notion of polynomial input-to-state stability for infinite-dimensional linear systems. This notion comes from polynomial stability of $C_0$-semigroups. We obtain sufficient conditions for polynomial input-to-state stability, by restricting the range of an input operator. Necessary conditions for polynomial input-to-state stability and an attractivity property related to polynomial input-to-state stability are also investigated.

中文翻译：

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无限维线性系统的多项式输入状态稳定性

我们为无限维线性系统引入多项式输入到状态稳定性的概念。这个概念来自 $C_0$-半群的多项式稳定性。通过限制输入算子的范围，我们获得了多项式输入到状态稳定性的充分条件。还研究了多项式输入到状态稳定性的必要条件和与多项式输入到状态稳定性相关的吸引力特性。