Solvability and Approximate Solutions for the Robust Stabilization with Nominal and Robust Sensitivity Constraints

Multiplicative plant perturbations with H^¿-norm bounds are considered. The results of [9] are applied to the problem of robust stabilization with nominal sensitivity being less than some prespecified value and the robust performance (sensitivity) problem with a guaranteed stability robustness margin. A necessary and sufficient condition for the solvability of the first problem and a sufficient condition for the second problem are derived. Synthesis algorithms are given to construct real rational proper compensators satisfying our multiple design specifications.