Volume 12, Issue 1, February 2005, Pages 53 - 72
An L2 Norm Trajectory-Based Local Linearization for Low Order Systems
Received 24 November 2003, Accepted 27 April 2004, Available Online 1 February 2005.
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- 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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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 -