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In this note, we describe the generator of the modulus semigroup of the C 0-semigroup associated with the delay equation u (t) = Au(t) + Lu t , t 0,
— In this paper, admissibility of control operators for perturbed semigroups is considered. We prove that the set of admissible control operators for a semigroup generator is unchanged if we perturb this generator by an appropriate class of unbounded operators. The result is applied to prove the well-posedness of a class of time-delay systems.
We introduce polynomial stabilizability and detectability of well-posed systems in the sense that a feedback produces a polynomial stable C0–semigroup. Using these concepts, the polynomial stability of the given C0–semigroup governing the state equation can be characterized via polynomial bounds on the transfer function. We further give sufficient… (More)
This paper is devoted to the study of the approximate positive controllability for linear systems with positive boundary controls. The results are applied to an abstract transport equation and controlled flows in networks.