Real robustness bounds using generalized stability multipliers

Su cient conditions for robust stability using generalized stability multipliers are presented for systems with sectorand norm-bounded, block-structured real uncertainty. Two parametrizations of the multiplier are considered and the robustness criteria are written as linear matrix inequalities. Upper bounds for the peak structured singular value over frequency, which eliminate frequency gridding, are then derived. Numerical examples provide a comparison of the peak upper bounds obtained using the two multiplier parametrizations. These examples show that the conservatism of the peak upper bounds is reduced by increasing the dynamic order of the multiplier.