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Bounding L2 gain system error generated by approximations of the nonlinear vector field

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3 Author(s)
Kin Cheong Sou ; Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, 02139, USA ; Alexandre Megretski ; Luca Daniel

Typical nonlinear model order reduction approaches need to address two issues: reducing the order of the model, and approximating the vector field. In this paper we focus exclusively on the second issue, and present results characterizing the repercussions at the system level of vector field approximations. The error assessment problem is formulated as the L2 gain upper bounding problem of a scaled feedback interconnection. Applying the small gain theorem in the proposed setup, we prove that the L2 gain of the error system is upper bounded by the L2 gain of the vector field approximation error, provided it is small. In addition, the paper also presents a numerical procedure, based on the IQC/LMI approach, to perform the error estimation task with less conservatism. A numerical example is given in this paper to demonstrate the practical implications of the presented results.

Published in:

2007 IEEE/ACM International Conference on Computer-Aided Design

Date of Conference:

4-8 Nov. 2007