Duality Bounds in Robustness Analysis**The original version of this paper was presented at the 13th IFAC World Congress, which was held in San Francisco, U.S.A., during June 30 – July 5, 1996. The published proceedings of this IFAC meeting may be ordered from: Elsevier Science Limited, The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, UK. This paper was recommended for publication in revised form by Associate Editor Roberto Tempo under the direction of Editor Ruth. F. Curtain,11Duality theory is used to obtain bounds for an important class of infinite-dimensional optimization problems in robustness analysis.