Strong input-to-state stability for infinite-dimensional linear systems
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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.
KeywordsInput-to-state stability Integral input-to-state stability \(C_0\)-semigroup Infinite-time admissibility Orlicz space Infinite-dimensional systems
The authors would like to thank Birgit Jacob for valuable discussions and helpful comments on the manuscript. They are also very grateful to the anonymous referees for their careful reading of the manuscript and their suggestions for improvements.
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