# Article

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Keywords:
time-delay system; observability
Summary:
This paper presents some recent results about the design of observers for time-delay systems. It is focused on methods that can lead to design some useful observers in practical situations. First the links between observability properties and observers design is emphasized. Then some necessary and sufficient conditions and a method are provided to obtain unknown input observers for time-delay systems. Furthermore some $H_{\infty }$ design using Lyapunov–Krasovskii and Lyapunov–Razumikhin theories are presented and compared. Finally a polynomial approach based on the parametrization of all observers is proposed that allows to design robust observers for systems including unstructured uncertainties.
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