Design of stable controllers attaining low Hinfinity weighted sensitivity

Strong stabilization and sensitivity reduction for a linear time-invariant single-input single-output system are considered. Stable controllers are practically desirable in the presence of possible actuator or sensor failures. It is verified precisely that the optimal controller of H^infinity weighted sensitivity minimization is almost always unstable when the plant has more than two zeros in the right-half plane. An algorithm for attaining the low sensitivity property for stable controllers is presented. It is based on Nevanlinna-Pick interpolation.