Global stability in a system using echo for position control

Bartha, Ferenc A. and Krisztin, Tibor: Global stability in a system using echo for position control. Electronic journal of qualitative theory of differential equations : special edition, (3) 40. pp. 1-16. (2018)

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Abstract

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.

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