Hans Zwart (Corresponding Author), Birgit Jacob, Olof Staffans

17 Citations (Scopus)

## 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.
Original language English 341-350 19 Systems and control letters 48 3-4 https://doi.org/10.1016/S0167-6911(02)00277-3 Published - 15 Mar 2003

## Keywords

• $C_0$-semigroup
• Conditional basis
• MSC-93C25
• Infinite-dimensional system