 where
 where  , this note states and proves necessary and sufficient conditions under which a)
 , this note states and proves necessary and sufficient conditions under which a)  is an estimate of a linear function of
 is an estimate of a linear function of  (i.e.,
 (i.e.,  estimates
 estimates  ), or b) a linear function of
 ), or b) a linear function of  is an estimate of
 is an estimate of  (i.e.,
 (i.e.,  estimates
 estimates  ). The mapping
 ). The mapping  has been used previously by the authors to compute the estimator-controller form of a compensator whose state vector
 has been used previously by the authors to compute the estimator-controller form of a compensator whose state vector  had the same dimension as the plant state vector
 had the same dimension as the plant state vector  .
 .