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Characterization of " low-pass filtering " for some nonlinear ODE's

Samer Riachy 1, 2
1 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : The characterization of low-pass linear filters is nowadays a simple question relying on eigenvalue criteria, Bode diagram, Nyquist or Nichols plots. For nonlinear systems, the problem is more tricky. The present work tempts to develop a methodology for the characterization of " low-pass filtering " for nonlinear systems. Inspired by the DiPerna-Lions theory and relying on the theory of characteristics, the proposed method associates to the nonlinear ODE a linear transport PDE. A characterization of " low-pass filtering " is then deduced from developments on the PDE. Smooth ODE's of the form \dot{x} = F (x) are considered where the vector field F (x) is perturbed by an additive, rapidly oscillating, noise m which may have a big magnitude F (x + m). An intuitive observation is proved in this first contribution: if F has bounded derivatives, then the sensitivity of x to m decreases as the bound gets smaller or as m fluctuates faster.
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Submitted on : Tuesday, September 12, 2017 - 4:19:44 PM
Last modification on : Wednesday, July 21, 2021 - 2:16:02 PM
Long-term archiving on: : Wednesday, December 13, 2017 - 3:12:24 PM


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  • HAL Id : hal-01586248, version 1


Samer Riachy. Characterization of " low-pass filtering " for some nonlinear ODE's. IFAC WC 2017, Jul 2017, Toulouse, France. ⟨hal-01586248⟩



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