2000 character limit reached
Boundary feedback stabilization by piecewise constant time delay for the wave equation (1006.2212v1)
Published 11 Jun 2010 in math.OC and math.DS
Abstract: 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.