Model validation and a generalization of mu

The problem of finding a valid model in robust control theory is considered. The set of possible models is rich, and the problem is to determine whether, given one of these models with both additive noise and norm-bounded perturbations, and given experimental data, it is possible that the model could produce the observed input/output data. Model validation is reformulated as a generalization of the structured singular value, mu . The rho (QM) lower bound to standard mu is extended to a lower bound for the generalization of mu . The upper bound is formulated as a linear matrix inequality where the solution matrices are block structured, with some blocks positive definite and other blocks negative definite.<>