Observability and observers for a class of linear systems with delays

A brief description of observability, detectability, and spectral observability concepts for time-delay systems is given and some results on relations between these concepts are presented. Another result of this correspondence is the derivation of constructive design procedures for dynamic observers for a large class of linear autonomous systems with time delays. This class includes systems with arbitrary output (measurement) delays where the procedure is based on well-known methods of spectrum assignment for a pair of real matrices. It is also shown that the observer problem for general systems with delays can be reformulated so as to get an easier case without output delays.