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• W2019941698 abstract "Abstract Let A be a generator of a strongly continuous semigroup of operators, and assume that C and H are operators such that A + CH generates a strongly continuous semigroup SH(t) on X. Let λ0 be a real number in the resolvent set of A, and let ϱ ϵ [−1, 1]. Then there are some fairly unrestrictive conditions under which A+(λ0 − A)ϱCH(λ0 − A)−ϱ also generates a strongly continuous semigroup SK(t) on X which has the same exponential growth rate as SH(t). Given an input operator B, we can use this to identify a class of feedback perturbations K such that A + BK generates a strongly continuous semigroup. We can also use this result to identify classes of feedbacks which can and cannot uniformly stabilize a system. For example, we show that if the control on a cantilever beam in the state space H02[0, 1] × L2[0, 1] is a moment force on the free end, then we cannot stabilize the beam with an A − 1 2 - bounded feedback, but we can find an A e− 1 4 - bounded feedback, for any e > 0, which does stabilize the beam." @default.
• W2019941698 created "2016-06-24" @default.
• W2019941698 creator A5082625544 @default.
• W2019941698 date "1990-04-01" @default.
• W2019941698 modified "2023-09-27" @default.
• W2019941698 title "Semigroup generation and stabilization by Aϱ-bounded feedback perturbations" @default.
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• W2019941698 doi "https://doi.org/10.1016/0167-6911(90)90054-x" @default.
• W2019941698 hasPublicationYear "1990" @default.
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