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

TL;DR

This paper investigates strong input-to-state stability for infinite-dimensional linear systems, establishing conditions under which certain stability properties hold, especially focusing on admissibility in Orlicz spaces.

Contribution

It introduces sufficient conditions for strong integral input-to-state stability in infinite-dimensional systems using Orlicz space admissibility, highlighting differences from exponential stability cases.

Findings

Infinite-time admissibility in Orlicz spaces suffices for strong integral input-to-state stability.

Admissibility in Orlicz spaces is not necessary for stability in non-exponentially stable systems.

The paper clarifies the relationship between admissibility and stability in infinite-dimensional linear systems.

Abstract

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