Exponential decay of oscillations in a multidimensional delay differential system

Eugenii Shustin

doi:10.3934/proc.2003.2003.809

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2003, Volume 2003: 809-816. Doi: 10.3934/proc.2003.2003.809 open access

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Exponential decay of oscillations in a multidimensional delay differential system

Eugenii Shustin^1,

1.
School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, 69978 Tel Aviv

Received: July 31, 2002

Revised: March 31, 2003

Published: March 2003

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Abstract

We consider a multi-dimensional dynamical system with a discontinuous delayed part, which is a model of a relay type negative feedback with an uncertain time delay. Our main result consists of a sufficient criterion for an exponential decay of oscillations even when the non-delayed part of the system has no stable solutions.

Keywords:

delay differential equations,
adaptive relay control.

Mathematics Subject Classification: 34K11, 34K13, 34K35.

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