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On the nonuniqueness of singular value functions and balanced nonlinear realizations

✍ Scribed by W.Steven Gray; Jacquelien M.A. Scherpen

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
374 KB
Volume
44
Category
Article
ISSN
0167-6911

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✦ Synopsis

The notion of balanced realizations for nonlinear state space model reduction problems was ΓΏrst introduced by Scherpen in 1993. Analogous to the linear case, the so-called singular value functions of a system describe the relative importance of each state component from an input-output point of view. In this paper it is shown that the procedure for nonlinear balancing has some interesting ambiguities that do not occur in the linear case. SpeciΓΏcally, distinct sets of singular value functions and balanced realizations are possible.

πŸ“œ SIMILAR VOLUMES

On the Singular Values of the Drinfeld M
On the Singular Values of the Drinfeld Modular Function ΞΌ
✍ Daeyeol Jeon; Chang Heon Kim πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 118 KB

In this work we find a uniformizer m of the Drinfeld modular curve X 0 (T) and prove that singular values of m generate ring class fields over an imaginary quadratic field.