Estimating the plant state from the compensator state

This Note states and proves a necessary and sufficient condition under which an estimate x?? of x can be expressed as a linear function of z, x?? = Tz, in the system w = Sw where w = (x z). The mapping T was used in [2] to compute the estimator-controller form of a compensator whose state vector z had the same dimension as the plant state vector x.