BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Input to state stability of evolution equations Jacob, Birgit


In this talk we study the notions of input to state stability (ISS) and integral input to state stability (iISS) for boundary control systems, which are stronger notions than exponential stability of the corresponding semigroup and include stability with respect to input functions as well. It will be shown that if the semigroup is exponentially stable, then ISS is equivalent to admissibility of the input operator with respect to $L^\infty$ . Further, under the assumption of exponential stability iISS is just admissibility of the input operator with respect to an Orlicz space. Further, we prove that for parabolic systems ISS and iISS are equivalent notions.

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