An observer design for linear time-delay systems

An observer design is proposed for linear systems with time delays. The key to the design is to find a generalized coordinate change such that, in the new coordinates, all the time-delay terms are injected by the system's output. The existence of such a coordinate change is guaranteed by a rank condition on the observability matrix. The novelty of the proposed design is clearly reflected in the multiple-output case, where a dimensional expansion in the coordinate change could become necessary, and hence is allowed.