Observers and duality between observation and state feedback for time delay systems

This paper deals with the problem of observer construction for systems with general time-delays in state and output. The spectrum of the infinitesimal generator of the observer semigroup is determined explicitly, and the observer equation is decomposed into a finite- and an infinite-dimensional component. For systems with delays appearing in the state variables only duality results are obtained and the observer is described in the more concrete form of a differential delay equation.