Design of Optimal Control Systems with Stable Feedback

The problem of stabilizing a single-input single-output system using stable feedback is considered. The performance index that is minimized is the weighted sensitivity of the closed-loop system to external disturbances. However, the resulting feedback associated with the minimum value of the optimality criterion turns out to be irrational. A design algorithm has been developed to find an approximation whose deviation from a sub-optimal system lies within a pre-specified error bound.