Journal of Nonlinear Mathematical Physics

Volume 12, Issue 1, February 2005, Pages 53 - 72

An L2 Norm Trajectory-Based Local Linearization for Low Order Systems

Authors
Fethi Belkhouche
Corresponding Author
Fethi Belkhouche
Received 24 November 2003, Accepted 27 April 2004, Available Online 1 February 2005.
DOI
https://doi.org/10.2991/jnmp.2005.12.1.6How to use a DOI?
Abstract
This paper presents a linear transformation for low order nonlinear autonomous diferential equations. The procedure consists of a trajectory-based local linearization, which approximates the nonlinear system in the neighborhood of its equilibria. The approximation is possible even in the non-hyperbolic case which is of a particular iterest. The linear system is derived using an L2 norm optimization and the method can be used to approximate the derivative at the equilibrium position. Unlike the classical linearization, the L2 norm linearization depends on the initial state and has the same order as the nonlinearity. Simulation results show good agreement of the suggested method with the nonlinear system.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
12 - 1
Pages
53 - 72
Publication Date
2005/02
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2005.12.1.6How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Fethi Belkhouche
PY  - 2005
DA  - 2005/02
TI  - An L2 Norm Trajectory-Based Local Linearization for Low Order Systems
JO  - Journal of Nonlinear Mathematical Physics
SP  - 53
EP  - 72
VL  - 12
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2005.12.1.6
DO  - https://doi.org/10.2991/jnmp.2005.12.1.6
ID  - Belkhouche2005
ER  -