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Strong Stability of Sampled-data Riesz-spectral Systems

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Document pages: 24 pages

Abstract: Suppose that a continuous-time linear infinite-dimensional system with astatic state-feedback controller is strongly stable. We address the followingquestion: If we convert the continuous-time controller to a sampled-datacontroller by applying an idealized sampler and a zero-order hold, will theresulting sampled-data system be strongly stable for all sufficient smallsampling periods? In this paper, we restrict our attention to the situationwhere the generator of the open-loop system is a Riesz-spectral operator andits point spectrum has a limit point at the origin. We present conditions underwhich the answer to the above question is affirmative. In the robustnessanalysis, we show that the sufficient condition for strong stability obtainedin the Arendt-Batty-Lyubich-Vũ theorem is preserved under sampling.

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