2005年
Algebraic structures of a rational-in-the-state representation after immersion
2005 44th IEEE Conference on Decision and Control & European Control Conference, Vols 1-8
- 巻
- 2005
- 号
- 開始ページ
- 4231
- 終了ページ
- 4236
- 記述言語
- 英語
- 掲載種別
- 研究論文(国際会議プロシーディングス)
- DOI
- 10.1109/CDC.2005.1582826
- 出版者・発行元
- IEEE
This paper discusses some algebraic structures and their geometric counterparts associated with a rational-in-the-state representation (RSR) and a polynomial-in-the-state representation (PSR) obtained via system immersion of a given nonlinear system. First, all of RSRs and PSRs obtained by an identical immersion are parameterized in terms of the relation ideal of the immersion. Second, the notions of an invariant ideal and an invariant variety of a nonlinear system over a ring are introduced, which are closely related to a differential algebraic equation. Then, it is shown that a RSR and a PSR have invariant ideals and invariant varieties associated with an immersion. In particular, an invariant variety of a RSR or a PSR is the Zariski closure of the image of the immersion, i.e., the smallest variety containing the image of the immersion.
- リンク情報
- ID情報
-
- DOI : 10.1109/CDC.2005.1582826
- ISSN : 0191-2216
- Web of Science ID : WOS:000240653704012