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This paper deals with strong versions of input-to-state stability andintegral input-to-state stability of infinite-dimensional linear systems withan unbounded input operator. We show that infinite-time admissibility withrespect to inputs in an Orlicz space is a sufficient condition for a system tobe strongly integral input-to-state stable but, unlike in the case ofexponentially stable systems, not a necessary one.

Strong input-to-state stability for infinite dimensional linear systems