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

  • Robert Nabiullin
  • Felix L. Schwenninger
Original Article


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.


Input-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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© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and Natural SciencesUniversity of WuppertalWuppertalGermany
  2. 2.Department of Mathematics, Center for Optimization and ApproximationUniversity of HamburgHamburgGermany

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