On the choice of inputs in identification for robust control

The thesis that noisy identification has close ties to the study of the sin gular-value decomposition of perturbed matrices is investigated. In particu lar by assuming an upper bound on the norm of the perturbation, one can obt ain a convex parametrization of an uncertain family of systems which contai ns the system generating the data. In this approach, the second-smallest si ngular value sigma(*) of an appropriately defined data matrix becomes a qua ntity of importance as it provides an upper bound for the size of the uncer tain family. This yields a new tool leading to the design of input function s which are optimal or persistently exciting from the point of view of iden tification for robust control. (C) 1999 Elsevier Science Ltd. All rights re served.