On the nonuniqueness of singular value functions and balanced nonlinear realizations

The notion of balanced realizations for nonlinear state space model reducti on problems was first introduced by Scherpen in 1993. Analogous to the line ar case, the so-called singular value functions of a system describe the re lative importance of each state component from an input-output point of vie w. In this paper it is shown that the procedure for nonlinear balancing has some interesting ambiguities that do not occur in the linear case. Specifi cally, distinct sets of singular value functions and balanced realizations are possible. (C) 2001 Elsevier Science B.V. All rights reserved.