On duality in robustness analysis

Frequency domain conditions involving multipliers is a powerful tool for robustness analysis. The resulting analysis problem is generally infinite dimensional and numerical solutions restricted to finite dimensional subspaces need to be considered. The finite dimensional problem can be transformed to a linear matrix inequality, which can be solved with efficient algorithms. This paper presents a format for the dual of the infinite dimensional problem. The dual can be used to investigate if the primal robustness problem is feasible. It can also be used to estimate the conservatism of a particular finite dimensional subspace of the primal