%0 Report
%T On Super-High-Frequencies in Discontinuous 1st-Order Delay-Differential Equations
%+ Mathematical and Computer Science Tools for Automatic Control (META2)
%+ Applications and Tools of Automatic Control (SOSSO)
%A Akian, Marianne
%A Bliman, Pierre-Alexandre
%Z Projet SOSSO, Projet META2
%N RR-3443
%I INRIA
%8 1998
%D 1998
%K SUPER-HIGH-FREQUENCY OSCILLATIONS
%K DELAY DIFFERENTIAL EQUATIONS
%K PERIODIC SOLUTIONS
%K SLOWLY OSCILLATING SOLUTIONS
%K RELAY NONLINEARITY
%Z Computer Science [cs]/Other [cs.OH]Reports
%X 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 FridmanĀ et al., any solution of the system under study coincides, after a finite time, with one of the periodic solutions.
%G English
%2 https://inria.hal.science/inria-00077201/document
%2 https://inria.hal.science/inria-00077201/file/RR-3443.pdf
%L inria-00077201
%U https://inria.hal.science/inria-00077201
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