Modal reduction guided by Hankel singular value intervals (with application to control design for compact disc players)

A simple procedure is proposed to find sets of modes that are input-output dominant. Hankel singular value intervals are derived that estimate the reachability-observability of sets of modes. Eigenvalue perturbation theory of Gersgorin is used to determine these intervals and to check that the reachability and observability Gramians of the modal realization approximate the diagonal Gramians of an internally balanced realization. The application of the technique to compact disc mechanism control design is briefly described.