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 (CRIStAL) - 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.
Type de document :
Communication dans un congrès
IFAC WC 2017, Jul 2017, Toulouse, France
Liste complète des métadonnées

Littérature citée [13 références]  Voir  Masquer  Télécharger
Contributeur : Samer Riachy <>
Soumis le : mardi 12 septembre 2017 - 16:19:44
Dernière modification le : mardi 3 juillet 2018 - 11:36:06
Document(s) archivé(s) le : mercredi 13 décembre 2017 - 15:12:24


Fichiers produits par l'(les) auteur(s)


  • 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〉



Consultations de la notice


Téléchargements de fichiers