An asymptotic observer for linear autonomous time lag systems

A full state vector observer is derived for a class of linear autonomous time lag systems, represented by differential equations. The major features of the approach are: (1) an observer is constructed just for the set of unstable or poorly damped modes of the delayed system once they have been determined; and (2) the design is done by using a partial-fraction expansion separating the unstable part from the system and then applying well-known finite dimensional state vector techniques. A procedure for the construction is given along with some numerical results to prove the simplicity of the observer