Jointly optimized error-feedback and realization for roundoff noise minimization in state-estimate feedback digital controllers

The joint optimization problem of error-feedback and realization for the closed-loop system with a state-estimate feedback digital controller is investigated where the main objective is to minimize the effects of roundoff noise at the closed-loop system output subject to l₂-norm dynamic-range scaling constraints. It is shown that the problem can be converted into an unconstrained optimization problem by using linear-algebraic techniques. The unconstrained optimization problem at hand is then solved iteratively by employing an efficient quasi-Newton algorithm with closed-form formulas for key gradient evaluation. Analytical details are given as to how the proposed technique can be applied to the cases where the error-feedback matrix is a general, diagonal, or scalar matrix. A numerical example is presented to illustrate the utility of the proposed technique.