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Robustness Issues of the Best Linear Approximation of a Nonlinear System

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5 Author(s)
Johan Schoukens ; Dept. Fundamental Electr. & Instrum. (ELEC), Vrije Univ. Brussel, Brussel ; John Lataire ; Rik Pintelon ; Gerd Vandersteen
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In many engineering applications, linear models are preferred, even if it is known that the system is disturbed by nonlinear distortions. A large class of nonlinear systems, which are excited with a ldquoGaussianrdquo random excitation, can be represented as a linear system G BLA plus a nonlinear noise source Y S . The nonlinear noise source represents that part of the output that is not captured by the linear approximation. In this paper, it is shown that the best linear approximation G BLA and the power spectrum S Y S of the nonlinear noise source Y S are invariants for a wide class of excitations with a user-specified power spectrum. This shows that the alternative ldquolinear representationrdquo of a nonlinear system is robust, making its use in the daily engineering practice very attractive. This result also opens perspectives to a new generation of dynamic system analyzers that also provide information on the nonlinear behavior of the tested system without increasing the measurement time.

Published in:

IEEE Transactions on Instrumentation and Measurement  (Volume:58 ,  Issue: 5 )