  This paper studies the problem of designing sampled-data observers and
observer-based, sampled-data, output feedback stabilizers for systems with both
discrete and distributed, state and output time-delays. The obtained results
can be applied to time delay systems of strict-feedback structure, transport
Partial Differential Equations (PDEs) with nonlocal terms, and feedback
interconnections of Ordinary Differential Equations with a transport PDE. The
proposed design approach consists in exploiting an existing observer, which
features robust exponential convergence of the error when continuous-time
output measurements are available. The observer is then modified, mainly by
adding an inter-sample output predictor, to compensate for the effect of
data-sampling. Using Lyapunov stability tools and small-gain analysis, we show
that robust exponential stability of the error is preserved, provided the
sampling period is not too large. The general result is illustrated with
different examples including state observation and output-feedback
stabilization of a chemical reactor.
