State variable reconstruction of delay systems

Consider the single-input single-output delay system with a single delay X(t) = A(d) X(t) + B u(t) (I) y(t) = C X(t) where X(t) = ??(t), t??[-h,0] A(d) = Ao + A1d, dX(t) = X(t-h) X(t)??Rn, u(t)??R1 and y(t)??R1. The problem is to find the state variable vector X(t) from the output variable y and the control input u. Unfortunately, the exact reconstruction method for non-delay systems, which was proposed by Chyung [1], cannot be directly applied to the delay systems. However, if the delay system is transformed into an equivalent system where only the output variable y is delayed, then the reconstruction method can be extended to cover the delay systems. The transformation is possible if the delay system is R[d]-observable (observable over R[d]).