Efficient computation of the multiplier based μ upper bound on large frequency intervals

An algorithm for computing and validating the multiplier based μ upper bound of Fu and Barabanov (1997) on large frequency intervals is developed in this paper. It avoids the use of a frequency grid and removes the risk of missing a critical frequency. The μ-sensitivities are also introduced as a way to evaluate which uncertainties are worth considering when optimizing the multiplier. This allows to drastically reduce the computation time with only a slight loss of accuracy. The proposed technique is validated on three benchmarks and gives an interesting alternative to the classical (D,G)-scalings based μ upper bound when the latter is too conservative.