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Reports (Research Report) Year : 1998

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

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.
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Dates and versions

inria-00077201 , version 1 (29-05-2006)

Identifiers

  • HAL Id : inria-00077201 , version 1

Cite

Marianne Akian, Pierre-Alexandre Bliman. On Super-High-Frequencies in Discontinuous 1st-Order Delay-Differential Equations. [Research Report] RR-3443, INRIA. 1998. ⟨inria-00077201⟩
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