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

DOI

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.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Fethi Belkhouche
PY  - 2005
DA  - 2005/02/01
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  - 10.2991/jnmp.2005.12.1.6
ID  - Belkhouche2005
ER  -