A new functional analytic approach to the concept of feedback stabilizability of infinite dimensional linear neutral systems is presented. We first reformulate this systems as an infinite dimensional open-loop systems with appropriate semigroups and unbounded control operators. We introduce conditions for which such semigroups are eventually compact. In addition, when the image of the control operator is finite dimensional, we give necessary and sufficient conditions for the feedback stabilizability of neutral system. Our approach is based on the concept of regular linear systems in the Salamon-Weiss sens.
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Hadd et al. (2010) studied this question.
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