Comments on "Controller design with multiple objectives"

We point out that the proof of one of the theorems presented in the above paper by Elia et al. (see ibid. vol.42 (1997)) is invalid and provide a correct proof. The flawed proof is long and complex, and incorrectly tries to make use of duality results via a version of the Lagrange multiplier theorem. The proof we presented, based on an elementary convexity argument, is very simple.