A generalization of the structured singular value and its application to model validation

The structured singular value μ gives a means of assessing the stability and performance of a system under a class of norm-bounded structured perturbations. This paper introduces a generalization of μ which guarantees stability with respect to perturbations, where some elements of the perturbation structure are bounded from above and some are bounded from below. This generalization is used to solve the frequency domain robust control model validation problem. Model validation determines whether or not there exist a model in the model set and a bounded noise signal that are consistent with the experimental input-output measurements. A computable convex upper bound to the generalized μ problem is presented, and the relationship between the generalized μ problem and the standard μ and model validation problems is discussed