H_∞-Optimization without Assumptions on Finite or Infinite Zeros

Explicit algebraic conditions are presented for the suboptimality of some parameter in the H_∞-optimization problem by output measurement control. Apart from two strict properness conditions, no artificial assumptions restrict the underlying system. In particular, the plant may have zeros on the imaginary axis or at infinity. These suboptimality characterizations are applied to show how to compute the optimal value by quadratically convergent algorithms and to solve the almost disturbance decoupling problem with internal stability.