  Given a plant subject to delayed sensor measurement, there are several
approaches to compensate for the delay. An obvious approach is to address this
problem in state space, where the $n$-dimensional plant state is augmented by
an $N$-dimensional (Pad\'e) approximation to the delay, affording (optimal)
state estimate feedback vis-\`a-vis the separation principle. Using this
framework, we show: (1) Feedback of the estimated plant states partially
inverts the delay; (2) The optimal (Kalman) estimator decomposes into $N$
(Pad\'e) uncontrollable states, and the remaining $n$ eigenvalues are the
solution to a reduced-order Kalman filter problem. Further, we show that the
tradeoff of estimation error (of the full state estimator) between plant
disturbance and measurement noise, only depends on the reduced-order Kalman
filter (that can be constructed independently of the delay); (3) A subtly
modified version of this state-estimation-based control scheme bears close
resemblance to a Smith predictor. This modified state-space approach shares
several limitations with its Smith predictor analog (including the inability to
stabilize most unstable plants), limitations that are alleviated when using the
unmodified state estimation framework.
