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arXiv · 1709.08276

On the admissibility of retarded delay systems

Radoslaw Zawiski·Jonathan R. Partington
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Abstract

We investigate a Hilbert space dynamical system of the form $\dot{z}(t)=Az(t)+A_1z(t-\tau)+Bu(t)$, where $A$ generates a semigroup of contractions and $A_1$ is a bounded operator, in order to determine whether the operator $B$ is admissible. Our approach is based on the Miyadera--Voigt perturbation theorem and the Weiss conjecture on admissibility of control operators for contraction semigroups. We demonstrate that the retarded delay system can be represented as a well-posed abstract Cauchy problem with a solution formed by an initially log-concave bounded semigroup.

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Radoslaw Zawiski, Jonathan R. Partington. 2017-09-24. On the admissibility of retarded delay systems. https://arxiv.org/abs/1709.08276

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