Global transformations of nonlinear systems

Author

Hunt, L.R. ; Su, Renjeng ; Meyer, George

Author_Institution

Texas Tech University, Lubbock, TX, USA

Volume

Issue

fYear

1983

fDate

1/1/1983 12:00:00 AM

Firstpage

Lastpage

Abstract

Recent results have established necessary and sufficient conditions for a nonlinear system of the form $\\dot{x}(t) = f(x(t))-u(t)g(x(t))$ . with $f(0) = 0$ , to be locally equivalent in a neighborhood of the origin in Rⁿto a controllable linear system. We combine these results with several versions of the global inverse function theorem to prove sufficient conditions for the transformation of a nonlinear system to a linear system. In doing so we introduce a technique for constructing a transformation under the assumptions that $\\{g.[f.g],\\cdots ,(ad^{n-1}f.g)\\$ span an $n$ -dimensional space and that $\\{g.[f.g],\\cdots ,(ad^{n-2}f.g)\\$ is an involutive set.

Keywords

Nonlinear systems; Aerospace control; Ear; Feedback; Jacobian matrices; Linear systems; NASA; Nonlinear systems; Partial differential equations; Stability; Sufficient conditions;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.1983.1103137

Filename

1103137

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=840789