Title :
Differentially algebraic immersion of nonlinear systems into rational-in-the-state representations
Author :
Ohtsuka, Toshiyuki
Author_Institution :
Dept. of Comput.-Controlled Mech. Syst., Osaka Univ., Suita, Japan
Abstract :
A system immersion is a mapping of an initial state such that two different systems have an identical input-output mapping. This paper considers a particular class of system immersion, called differentially algebraic (DA) immersion, which is suitable to investigate geometric characteristics of a system after immersion. It is shown that a given system is DA immersible into a polynomial-in-the-state representation (PSR) if and only if it is so into a rational-in-the-state representation (RSR). Then, necessary and sufficient conditions are given for DA immersibility into a RSR in terms of differential algebraic structure of the state equation. Some examples are given to highlight differences between related theoretical results.
Keywords :
nonlinear systems; optimisation; differential algebraic structure; differentially algebraic immersion; geometric characteristics; input-output mapping; necessary and sufficient conditions; nonlinear systems; polynomial-in-the-state representation; rational-in-the-state representations; state equation; system immersion; Differential algebraic equations; Linear systems; Mechanical systems; Nonlinear equations; Nonlinear systems; Polynomials; State estimation; State feedback; Sufficient conditions; System identification;
Conference_Titel :
Decision and Control, 2002, Proceedings of the 41st IEEE Conference on
Print_ISBN :
0-7803-7516-5
DOI :
10.1109/CDC.2002.1184255
