Optimal finite precision implementation of a state-estimate feedback controller

Expressions are derived for the sensitivity and the roundoff noise gain of the closed-loop transfer function of a system when the state estimate feedback controller is implemented with a finite word length and when the computations are performed in finite precision. This allows one to compare the sensitivity and noise gain over all equivalent state-variable implementations of the observer plus controller. The set of state-space models minimizing either the sensitivity or the roundoff noise gain is computed. Simulations compare the performance of the optimal implementations with respect to companion forms and a particular delta model