%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 %~ INRIA %~ INRIA-ROCQ %~ INRIA-RRRT %~ INRIA_TEST %~ TESTALAIN1 %~ INRIA2 %~ LARA