Polynomial Input-to-state Stability of Infinite-dimensional Linear Systems.

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.