This paper deals with strong versions of input-to-state stability for infinite-dimensional linear systems with an unbounded control operator. We show that strong input-to-state stability with respect to inputs in an Orlicz space is a sufficient condition for a system to be strongly integral input-to-state stable with respect to bounded inputs. In contrast to the special case of systems with exponentially stable semigroup, the converse fails in general.
- Infinite-dimensional systems
- Infinite-time admissibility
- Input-to-state stability
- Integral input-to-state stability
- Orlicz space