Duality in multiplier-based robustness analysis

Frequency domain conditions involving multipliers are useful for robustness analysis. The resulting analysis problem is generally convex, but infinite-dimensional and numerical solutions restricted to finite-dimensional subspaces need to be considered. The resulting finite-dimensional problem can be transformed into a linear matrix inequality, which can be solved using efficient algorithms. The paper presents a format for the dual of the infinite-dimensional problem. The dual problem can be used to estimate the conservatism of particular finite-dimensional subspaces.