8485 articles  [version française]

inria-00077201, version 1

On Super-High-Frequencies in Discontinuous 1st-Order Delay-Differential Equations

Marianne Akian () 1, Pierre-Alexandre Bliman 2

N° RR-3443 (1998)

Abstract: One considers a scalar 1st-order nonlinear differential equation with a delayed relay-output proportional feedback. One shows that, under a boundedness condition on the nonlinearity only, any solution of this equation has, after a finite time, a finite number of zeros on compact sets. An estimate of the time after which the super-high-frequency disappears is provided. This improves some previous works by Shustin. As a consequence, using some works by Fridman et al., any solution of the system under study coincides, after a finite time, with one of the periodic solutions.

  • 1:  META2 (INRIA Rocquencourt)
  • INRIA
  • 2:  SOSSO (INRIA Rocquencourt)
  • INRIA
  • Domain : Computer Science/Other
  • Keywords : SUPER-HIGH-FREQUENCY OSCILLATIONS / DELAY DIFFERENTIAL EQUATIONS / PERIODIC SOLUTIONS / SLOWLY OSCILLATING SOLUTIONS / RELAY NONLINEARITY
  • Internal note : RR-3443
  • Comment : Projet SOSSO – Projet META2
 
  • inria-00077201, version 1
  • http://hal.inria.fr/inria-00077201
  • oai:hal.inria.fr:inria-00077201
  • From: Rapport De Recherche Inria <>
  • Submitted on: Monday, 29 May 2006 17:19:13
  • Updated on: Wednesday, 18 April 2007 12:40:40