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Stabilizing effect of delay distribution for a class of second­order systems without instantaneous feedback

Stabilizing effect of delay distribution for a class of second­order systems without instantaneous feedback,http://www.tandfonline.com/doi/abs/10.1080

Stabilizing effect of delay distribution for a class of second­order systems without instantaneous feedback   (Citations: 1)
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In many situations in physics, engineering and biology time delays arise naturally due to the time needed to transport information from one part of the system to another and/or to react to incoming information. When differential equations are used in the mathematical modeling, then incorporating time delays leads to a description by a delay differential equation. We consider here a class of second­order scalar delay equations without instantaneous feedback, where the delays enter according to a distribution function. This is a natural description whenever there are more than one delay. In this paper we show that for this class of systems one can derive stability information about the distributed­delay system by considering the one delay system where the delay is the mean delay of the distribu­ tion function. More specifically, we prove that the asymptotic stability of the zero solution of the second­order delay equation with symmetric delay distribution is implied by the stability of the associated mean­delay equation. Our proof is based on the comparison of stability charts of the two equations.
Published in 2011.
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