Weak admissibility does not imply admissibility for analytic semigroups


Zwart, Hans and Jacob, Birgit and Staffans, Olof (2003) Weak admissibility does not imply admissibility for analytic semigroups. Systems & control letters, 48 (3-4). pp. 341-350. ISSN 0167-6911

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Abstract:Two conjectures on admissible control operators by George Weiss are disproved in this paper. One conjecture says that an operator $B$ defined on an infinite-dimensional Hilbert space $U$ is an admissible control operator if for every element $u \in U$ the vector $Bu$ defines an admissible control operator. The other conjecture says that $B$ is an admissible control operator if a certain resolvent estimate is satisfied. The examples given in this paper show that even for analytic semigroups the conjectures do not hold. In the last section we construct a semigroup example showing that the first estimate in the Hille-Yosida theorem is not sufficient to conclude boundedness of the semigroup.
Item Type:Article
Copyright:© 2003 Elsevier
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/68872
Official URL:https://doi.org/10.1016/S0167-6911(02)00277-3
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