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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Rapport
[Research Report] RR-3443, INRIA. 1998
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Dernière modification le : mardi 17 avril 2018 - 11:31:53
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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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