The thesis that noisy identification has close ties to the study of the singular-value decomposition of perturbed matrices is investigated. In particular by assuming an upper bound on the norm of the perturbation, one can obtain a convex parametrization of an uncertain family of systems which contains the system generating the data. In this approach, the second-smallest singular value sigma(*) of an appropriately defined data matrix becomes a quantity of importance as it provides an upper bound for the size of the uncertain family. This yields a new tool leading to the design of input functions which are optimal or persistently exciting from the point of view of identification for robust control.