Global stability in a system using echo for position control

We consider a system of equations describing automatic position control by echo. The system can be reduced to a single differential equation with state-dependent delay. The delayed terms come from the control mechanism and the reaction time. H.-O. Walther [Differ. Integral Equ. 15(2002), No. 8, 923–...

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Bibliographic Details
Main Authors: Bartha Ferenc A.
Krisztin Tibor
Format: Serial
Published: 2018
Series:Electronic journal of qualitative theory of differential equations
Kulcsszavak:Differenciálegyenlet
doi:10.14232/ejqtde.2018.1.40

Online Access:http://acta.bibl.u-szeged.hu/58145
Description
Summary:We consider a system of equations describing automatic position control by echo. The system can be reduced to a single differential equation with state-dependent delay. The delayed terms come from the control mechanism and the reaction time. H.-O. Walther [Differ. Integral Equ. 15(2002), No. 8, 923–944] proved that stable periodic motion is possible for large enough reaction time. We show that, for sufficiently small reaction lag, the control is perfect, i.e., the preferred position of the system is globally asymptotically stable.
Physical Description:1-16
ISSN:1417-3875