Birgit Jacob

Admissibility of Control and Observation Operators for Semigroups: A Survey

This paper reviews the literature on admissibility of control and observation operators for semigroups, presenting many recent results in this approach to infinite-dimensional systems theory. The themes discussed include duality between control and observation, conditions for admissibility expressed in terms of the resolvent of the infinitesimal generator, results for normal semigroups and their links with Carleson measures, properties of shift semigroups and Hankel operators, contraction semigroups and functional models, Hille-Yosida conditions on the resolvent, and weak admissibility.

Analyticity and Riesz basis property of semigroups associated to damped vibrations

Abstract.Second order equations of the form

Minimum-Phase Infinite-Dimensional Second-Order Systems

ddot{z}(t) + A_0z(t) + Ddot{z}(t) = 0

Semilinear observation systems

are considered. Such equations are often used as a model for transverse motions of thin beams in the presence of damping. We derive various properties of the operator matrix

DESCH-SCHAPPACHER PERTURBATION OF ONE-PARAMETER SEMIGROUPS ON LOCALLY CONVEX SPACES

mathcal{A} = left[ {begin{array}{*{20}c}n 0 & I { -A_0 } & { -D}nend{array}} right]

Observation of Volterra systems with scalar kernels

associated with the second order problem above. We develop sufficient conditions for analyticity of the associated semigroup and for the existence of a Riesz basis consisting of eigenvectors and associated vectors of