ℋ∞ servo design using complementary weightings

A method of ℋ_∞ servo system design which does not use unstable weightings has been proposed. An obvious approach to ℋ_∞ servo design is to use the weighting function with jω poles, though a significant difficulty arises since the rank conditions on the imaginary axis are not satisfied in the generalized plant. This infinity gain weighting specification can be transformed to another ℋ_∞-norm constraint using stable bounded “complementary weighting”. We show that the solution of the ℋ_∞ constraint with the complementary weighting satisfies the servo specification and the obtained controller contains an appropriate internal model