A Jacobi-type method for computing balanced realizations

A new numerical scheme for computing balancing coordinate transformations i n linear systems theory is presented. The method is closely related to the Jacobi method for diagonalizing symmetric matrices. Here the minimization o f the sum of traces of the Gramians by orthogonal and nonorthogonal Jacobi- type rotations is considered. The algorithm is shown to be globally converg ent to a balancing transformation that arranges the Hankel singular values in a prescribed ordering. Local quadratic convergence of the algorithm is s hown. (C) 2000 Elsevier Science B.V. All rights reserved.