Boundary feedback stabilization by piecewise constant time delay for the wave equation

Details Boundary feedback stabilization by piecewise constant time delay for the wave equation Boundary feedback stabilization by piecewise constant time delay for the wave equation

2010-06-11

arxiv.org/abs/1006.2212v1

Mathematics

Optimization and Control

18 pages

Scientific paper

For vibrating systems, a delay in the application of a feedback control can destroy the stabilizing effect of the control. In this paper we consider a vibrating string that is fixed at one end and stabilized with a boundary feedback with delay at the other end. We show that for certain feedback parameters the system is exponentially stable with constant delays of the form 4L/c, 8L/c, 12L/c ... Moreover, we show that the system is exponentially stable with piecewise constant delays that attain the values 4L/c and 8L/c.

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