ABSTRACT
Let S(t), t ≥ 0, denote a C 0-semigroup over a Hilbert space ℋ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187810/28005645-324c-4d25-a9e4-00a49a74dffd/content/inq_chapter4_43_1.tif"/> . We say that the semigroup is superstable if the indicator ω 0 = lim t → ∞ ( Log ‖ S ( t ) ‖ t ) = − ∞ . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187810/28005645-324c-4d25-a9e4-00a49a74dffd/content/inq_chapter4_43_2.tif"/>
In this paper we give an example of such a semigroup in the theory of “smart” structures. Specifically, we consider Timoshenko models of smart beams — beams with embedded sensor-actuator strips — with pure rate feedback, and show that there are no “modes” (eigenvalues) for a critical value of the feedback gain, the superstability being a consequence.
